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    Something a while ago made me wonder if people were interpretting the results of flattening the covid19 curve wrong.  Log graphs are good way to display a wide range of data in a compact way, but if you can't interpret it properly then you might as well think apples are oranges.  There was something someone said not to long ago that I didn't believe.  That person was Dr. Fauci, an American physician and immunologist who served as the director of the National Institute of Allergy and Infectious Diseases since 1984.  On April 9, 2020 he said, on the final death toll of the U.S. for Coronavirus, and I quote "looks more like 60,000 than the 100,000 to 200,000" U.S. officials had previously estimated ...  Back then I thought he was wrong, and actually now, he is wrong.

     

    Some people just don't understand log graphs and I believe a lot of people are misinterpretting them.  Take a linear graph increasing in time and put it on a log scale and you naturally get a "flattening" curve without even doing anything.  But let's see what Dr. Fauci was seeing, and how he and likely many others, are misinterpretting the graphs.

     

    Taking data from Worldometers.info/coronavirus we gather the total deaths

    ``

    USTotaldeathsdates := ["Feb 15", "Feb 16", "Feb 17", "Feb 18", "Feb 19", "Feb 20", "Feb 21", "Feb 22", "Feb 23", "Feb 24", "Feb 25", "Feb 26", "Feb 27", "Feb 28", "Feb 29", "Mar 01", "Mar 02", "Mar 03", "Mar 04", "Mar 05", "Mar 06", "Mar 07", "Mar 08", "Mar 09", "Mar 10", "Mar 11", "Mar 12", "Mar 13", "Mar 14", "Mar 15", "Mar 16", "Mar 17", "Mar 18", "Mar 19", "Mar 20", "Mar 21", "Mar 22", "Mar 23", "Mar 24", "Mar 25", "Mar 26", "Mar 27", "Mar 28", "Mar 29", "Mar 30", "Mar 31", "Apr 01", "Apr 02", "Apr 03", "Apr 04", "Apr 05", "Apr 06", "Apr 07", "Apr 08", "Apr 09", "Apr 10", "Apr 11", "Apr 12", "Apr 13", "Apr 14", "Apr 15", "Apr 16", "Apr 17", "Apr 18", "Apr 19", "Apr 20", "Apr 21", "Apr 22", "Apr 23", "Apr 24", "Apr 25", "Apr 26", "Apr 27", "Apr 28", "Apr 29", "Apr 30", "May 01"]:

    USTotalDeaths := [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 9, 11, 12, 15, 19, 22, 26, 30, 38, 41, 48, 58, 73, 95, 121, 171, 239, 309, 374, 509, 689, 957, 1260, 1614, 2110, 2754, 3251, 4066, 5151, 6394, 7576, 8839, 10384, 11793, 13298, 15526, 17691, 19802, 22038, 24062, 25789, 27515, 30081, 32712, 34905, 37448, 39331, 40901, 42853, 45536, 47894, 50234, 52191, 54256, 55412, 56795, 59265, 61655, 63856, 65753]:

    ``

    We will graph the data from when there were more than 100 deaths and up until April 9th when he made his prediction.

    ListTools:-Search("Apr 09", USTotaldeathsdates)

    55

    (1)

    ListTools:-Search(121, USTotalDeaths)

    32

    (2)

    with(plots):

    a := plots:-listplot(USTotalDeaths[32 .. 55], axis[2] = [mode = log], tickmarks = [[seq(i-31 = USTotaldeathsdates[i], i = 32 .. 55)], [100 = "100", 1000 = "1K", 10000 = "10K", 100000 = "100K", 1000000 = "1M"]], view = [default, 100 .. 1000000], color = "#FF9900", thickness = 6, labels = ["", "Total Coronavirus Deaths"], labeldirections = [default, vertical])

    PLOT(CURVES(Matrix(24, 2, {(1, 1) = 1.0, (1, 2) = 121.0, (2, 1) = 2.0, (2, 2) = 171.0, (3, 1) = 3.0, (3, 2) = 239.0, (4, 1) = 4.0, (4, 2) = 309.0, (5, 1) = 5.0, (5, 2) = 374.0, (6, 1) = 6.0, (6, 2) = 509.0, (7, 1) = 7.0, (7, 2) = 689.0, (8, 1) = 8.0, (8, 2) = 957.0, (9, 1) = 9.0, (9, 2) = 1260.0, (10, 1) = 10.0, (10, 2) = 1614.0, (11, 1) = 11.0, (11, 2) = 2110.0, (12, 1) = 12.0, (12, 2) = 2754.0, (13, 1) = 13.0, (13, 2) = 3251.0, (14, 1) = 14.0, (14, 2) = 4066.0, (15, 1) = 15.0, (15, 2) = 5151.0, (16, 1) = 16.0, (16, 2) = 6394.0, (17, 1) = 17.0, (17, 2) = 7576.0, (18, 1) = 18.0, (18, 2) = 8839.0, (19, 1) = 19.0, (19, 2) = 10384.0, (20, 1) = 20.0, (20, 2) = 11793.0, (21, 1) = 21.0, (21, 2) = 13298.0, (22, 1) = 22.0, (22, 2) = 15526.0, (23, 1) = 23.0, (23, 2) = 17691.0, (24, 1) = 24.0, (24, 2) = 19802.0}, datatype = float[8])), COLOUR(RGB, 1.00000000, .60000000, 0.), THICKNESS(6), _AXIS[2](_MODE(1)), AXESTICKS([1 = "Mar 17", 2 = "Mar 18", 3 = "Mar 19", 4 = "Mar 20", 5 = "Mar 21", 6 = "Mar 22", 7 = "Mar 23", 8 = "Mar 24", 9 = "Mar 25", 10 = "Mar 26", 11 = "Mar 27", 12 = "Mar 28", 13 = "Mar 29", 14 = "Mar 30", 15 = "Mar 31", 16 = "Apr 01", 17 = "Apr 02", 18 = "Apr 03", 19 = "Apr 04", 20 = "Apr 05", 21 = "Apr 06", 22 = "Apr 07", 23 = "Apr 08", 24 = "Apr 09"], [100 = "100", 1000 = "1K", 10000 = "10K", 100000 = "100K", 1000000 = "1M"]), AXESLABELS("", "Total Coronavirus Deaths", FONT(DEFAULT), DEFAULT, VERTICAL), VIEW(DEFAULT, 100 .. 1000000))

    (3)

    b := plot([1000, 10000, 100000, 1000000], x = 0 .. 30, color = "#E6E6E6", thickness = 0):

    ``

    NULL

     

    plots:-display(a, b, title = "Total Deaths \n (Logarithmic scale)\n", titlefont = ["Helvetica", 18], size = [681, 400])

     

    Just by looking at the graph you  can imagine Dr. Fauci saying look at that graph starting to level off and he would extrapolate an imaginary line that could if you wanted to level off around where he said 60,000.  And that's the confusion people have with these log graphs - people misinterpret them.  

    Here's what it looks like today

    a2 := plots:-listplot(USTotalDeaths[32 .. ()], axis[2] = [mode = log], tickmarks = [[seq(i-31 = USTotaldeathsdates[i], i = 32 .. nops(USTotaldeathsdates))], [100 = "100", 1000 = "1K", 10000 = "10K", 100000 = "100K", 1000000 = "1M"]], view = [default, 100 .. 1000000], color = "#FF9900", thickness = 6, labels = ["", "Total Coronavirus Deaths"], labeldirections = [default, vertical])

    PLOT(CURVES(Matrix(46, 2, {(1, 1) = 1.0, (1, 2) = 121.0, (2, 1) = 2.0, (2, 2) = 171.0, (3, 1) = 3.0, (3, 2) = 239.0, (4, 1) = 4.0, (4, 2) = 309.0, (5, 1) = 5.0, (5, 2) = 374.0, (6, 1) = 6.0, (6, 2) = 509.0, (7, 1) = 7.0, (7, 2) = 689.0, (8, 1) = 8.0, (8, 2) = 957.0, (9, 1) = 9.0, (9, 2) = 1260.0, (10, 1) = 10.0, (10, 2) = 1614.0, (11, 1) = 11.0, (11, 2) = 2110.0, (12, 1) = 12.0, (12, 2) = 2754.0, (13, 1) = 13.0, (13, 2) = 3251.0, (14, 1) = 14.0, (14, 2) = 4066.0, (15, 1) = 15.0, (15, 2) = 5151.0, (16, 1) = 16.0, (16, 2) = 6394.0, (17, 1) = 17.0, (17, 2) = 7576.0, (18, 1) = 18.0, (18, 2) = 8839.0, (19, 1) = 19.0, (19, 2) = 10384.0, (20, 1) = 20.0, (20, 2) = 11793.0, (21, 1) = 21.0, (21, 2) = 13298.0, (22, 1) = 22.0, (22, 2) = 15526.0, (23, 1) = 23.0, (23, 2) = 17691.0, (24, 1) = 24.0, (24, 2) = 19802.0, (25, 1) = 25.0, (25, 2) = 22038.0, (26, 1) = 26.0, (26, 2) = 24062.0, (27, 1) = 27.0, (27, 2) = 25789.0, (28, 1) = 28.0, (28, 2) = 27515.0, (29, 1) = 29.0, (29, 2) = 30081.0, (30, 1) = 30.0, (30, 2) = 32712.0, (31, 1) = 31.0, (31, 2) = 34905.0, (32, 1) = 32.0, (32, 2) = 37448.0, (33, 1) = 33.0, (33, 2) = 39331.0, (34, 1) = 34.0, (34, 2) = 40901.0, (35, 1) = 35.0, (35, 2) = 42853.0, (36, 1) = 36.0, (36, 2) = 45536.0, (37, 1) = 37.0, (37, 2) = 47894.0, (38, 1) = 38.0, (38, 2) = 50234.0, (39, 1) = 39.0, (39, 2) = 52191.0, (40, 1) = 40.0, (40, 2) = 54256.0, (41, 1) = 41.0, (41, 2) = 55412.0, (42, 1) = 42.0, (42, 2) = 56795.0, (43, 1) = 43.0, (43, 2) = 59265.0, (44, 1) = 44.0, (44, 2) = 61655.0, (45, 1) = 45.0, (45, 2) = 63856.0, (46, 1) = 46.0, (46, 2) = 65753.0}, datatype = float[8])), COLOUR(RGB, 1.00000000, .60000000, 0.), THICKNESS(6), _AXIS[2](_MODE(1)), AXESTICKS([1 = "Mar 17", 2 = "Mar 18", 3 = "Mar 19", 4 = "Mar 20", 5 = "Mar 21", 6 = "Mar 22", 7 = "Mar 23", 8 = "Mar 24", 9 = "Mar 25", 10 = "Mar 26", 11 = "Mar 27", 12 = "Mar 28", 13 = "Mar 29", 14 = "Mar 30", 15 = "Mar 31", 16 = "Apr 01", 17 = "Apr 02", 18 = "Apr 03", 19 = "Apr 04", 20 = "Apr 05", 21 = "Apr 06", 22 = "Apr 07", 23 = "Apr 08", 24 = "Apr 09", 25 = "Apr 10", 26 = "Apr 11", 27 = "Apr 12", 28 = "Apr 13", 29 = "Apr 14", 30 = "Apr 15", 31 = "Apr 16", 32 = "Apr 17", 33 = "Apr 18", 34 = "Apr 19", 35 = "Apr 20", 36 = "Apr 21", 37 = "Apr 22", 38 = "Apr 23", 39 = "Apr 24", 40 = "Apr 25", 41 = "Apr 26", 42 = "Apr 27", 43 = "Apr 28", 44 = "Apr 29", 45 = "Apr 30", 46 = "May 01"], [100 = "100", 1000 = "1K", 10000 = "10K", 100000 = "100K", 1000000 = "1M"]), AXESLABELS("", "Total Coronavirus Deaths", FONT(DEFAULT), DEFAULT, VERTICAL), VIEW(DEFAULT, 100 .. 1000000))

    (4)

    b2 := plot([1000, 10000, 100000, 1000000], x = 0 .. 60, color = "#E6E6E6", thickness = 0)

    PLOT(CURVES(Matrix(200, 2, {(1, 1) = .0, (1, 2) = 1000.0, (2, 1) = .3154563015075377, (2, 2) = 1000.0, (3, 1) = .5899331427135678, (3, 2) = 1000.0, (4, 1) = .8986110572864321, (4, 2) = 1000.0, (5, 1) = 1.2093350894472361, (5, 2) = 1000.0, (6, 1) = 1.5185823045226128, (6, 2) = 1000.0, (7, 1) = 1.8052940592964821, (7, 2) = 1000.0, (8, 1) = 2.102167474371859, (8, 2) = 1000.0, (9, 1) = 2.409194384924623, (9, 2) = 1000.0, (10, 1) = 2.7152366562814065, (10, 2) = 1000.0, (11, 1) = 3.0300387497487438, (11, 2) = 1000.0, (12, 1) = 3.3073166050251253, (12, 2) = 1000.0, (13, 1) = 3.6194657969849247, (13, 2) = 1000.0, (14, 1) = 3.9328967035175877, (14, 2) = 1000.0, (15, 1) = 4.234945459296482, (15, 2) = 1000.0, (16, 1) = 4.509234666331658, (16, 2) = 1000.0, (17, 1) = 4.835391063316583, (17, 2) = 1000.0, (18, 1) = 5.111688313567838, (18, 2) = 1000.0, (19, 1) = 5.433087699497487, (19, 2) = 1000.0, (20, 1) = 5.717580615075376, (20, 2) = 1000.0, (21, 1) = 6.029714433165829, (21, 2) = 1000.0, (22, 1) = 6.32693964120603, (22, 2) = 1000.0, (23, 1) = 6.63706296482412, (23, 2) = 1000.0, (24, 1) = 6.9218529859296485, (24, 2) = 1000.0, (25, 1) = 7.229037497487436, (25, 2) = 1000.0, (26, 1) = 7.548115872361809, (26, 2) = 1000.0, (27, 1) = 7.825874535678391, (27, 2) = 1000.0, (28, 1) = 8.125861501507536, (28, 2) = 1000.0, (29, 1) = 8.435777390954772, (29, 2) = 1000.0, (30, 1) = 8.738969626130652, (30, 2) = 1000.0, (31, 1) = 9.032323703517587, (31, 2) = 1000.0, (32, 1) = 9.358043390954773, (32, 2) = 1000.0, (33, 1) = 9.650717017085425, (33, 2) = 1000.0, (34, 1) = 9.963208582914572, (34, 2) = 1000.0, (35, 1) = 10.246372386934672, (35, 2) = 1000.0, (36, 1) = 10.555945218090452, (36, 2) = 1000.0, (37, 1) = 10.847229126633163, (37, 2) = 1000.0, (38, 1) = 11.151704740703517, (38, 2) = 1000.0, (39, 1) = 11.449385306532662, (39, 2) = 1000.0, (40, 1) = 11.761029271356783, (40, 2) = 1000.0, (41, 1) = 12.06117944924623, (41, 2) = 1000.0, (42, 1) = 12.368126357788944, (42, 2) = 1000.0, (43, 1) = 12.672531590954774, (43, 2) = 1000.0, (44, 1) = 12.952248385929648, (44, 2) = 1000.0, (45, 1) = 13.272835398994975, (45, 2) = 1000.0, (46, 1) = 13.55957224522613, (46, 2) = 1000.0, (47, 1) = 13.865293528643216, (47, 2) = 1000.0, (48, 1) = 14.157907806030149, (48, 2) = 1000.0, (49, 1) = 14.482818355778894, (49, 2) = 1000.0, (50, 1) = 14.76416701809045, (50, 2) = 1000.0, (51, 1) = 15.083500266331658, (51, 2) = 1000.0, (52, 1) = 15.374537855276381, (52, 2) = 1000.0, (53, 1) = 15.69288723919598, (53, 2) = 1000.0, (54, 1) = 15.967568918592962, (54, 2) = 1000.0, (55, 1) = 16.28039928844221, (55, 2) = 1000.0, (56, 1) = 16.582577981909548, (56, 2) = 1000.0, (57, 1) = 16.88455926934673, (57, 2) = 1000.0, (58, 1) = 17.18542962211055, (58, 2) = 1000.0, (59, 1) = 17.474471840201005, (59, 2) = 1000.0, (60, 1) = 17.786934132663315, (60, 2) = 1000.0, (61, 1) = 18.084733353768844, (61, 2) = 1000.0, (62, 1) = 18.398153011055275, (62, 2) = 1000.0, (63, 1) = 18.681873274371856, (63, 2) = 1000.0, (64, 1) = 18.995437278391957, (64, 2) = 1000.0, (65, 1) = 19.295776953768843, (65, 2) = 1000.0, (66, 1) = 19.595385593969848, (66, 2) = 1000.0, (67, 1) = 19.908327979899497, (67, 2) = 1000.0, (68, 1) = 20.19655934170854, (68, 2) = 1000.0, (69, 1) = 20.491747682412058, (69, 2) = 1000.0, (70, 1) = 20.817670685427135, (70, 2) = 1000.0, (71, 1) = 21.112767268341706, (71, 2) = 1000.0, (72, 1) = 21.414558798994975, (72, 2) = 1000.0, (73, 1) = 21.7214730120603, (73, 2) = 1000.0, (74, 1) = 22.003586897487438, (74, 2) = 1000.0, (75, 1) = 22.304311163819094, (75, 2) = 1000.0, (76, 1) = 22.602746297487435, (76, 2) = 1000.0, (77, 1) = 22.92197912562814, (77, 2) = 1000.0, (78, 1) = 23.20368826733668, (78, 2) = 1000.0, (79, 1) = 23.528722136683413, (79, 2) = 1000.0, (80, 1) = 23.822040144723616, (80, 2) = 1000.0, (81, 1) = 24.112262981909545, (81, 2) = 1000.0, (82, 1) = 24.42434576683417, (82, 2) = 1000.0, (83, 1) = 24.73769099095477, (83, 2) = 1000.0, (84, 1) = 25.022788748743714, (84, 2) = 1000.0, (85, 1) = 25.325549903517587, (85, 2) = 1000.0, (86, 1) = 25.6210152, (86, 2) = 1000.0, (87, 1) = 25.94130269849246, (87, 2) = 1000.0, (88, 1) = 26.21844043417085, (88, 2) = 1000.0, (89, 1) = 26.536743198994973, (89, 2) = 1000.0, (90, 1) = 26.835964531658288, (90, 2) = 1000.0, (91, 1) = 27.13229571256281, (91, 2) = 1000.0, (92, 1) = 27.428862627135675, (92, 2) = 1000.0, (93, 1) = 27.73134210753769, (93, 2) = 1000.0, (94, 1) = 28.05196528944723, (94, 2) = 1000.0, (95, 1) = 28.345945350753766, (95, 2) = 1000.0, (96, 1) = 28.636141420100497, (96, 2) = 1000.0, (97, 1) = 28.946356242211053, (97, 2) = 1000.0, (98, 1) = 29.255895753768844, (98, 2) = 1000.0, (99, 1) = 29.53372584723618, (99, 2) = 1000.0, (100, 1) = 29.862835628140704, (100, 2) = 1000.0, (101, 1) = 30.138219431155775, (101, 2) = 1000.0, (102, 1) = 30.46031172060301, (102, 2) = 1000.0, (103, 1) = 30.767717608040197, (103, 2) = 1000.0, (104, 1) = 31.042194449246228, (104, 2) = 1000.0, (105, 1) = 31.350872363819093, (105, 2) = 1000.0, (106, 1) = 31.661596395979895, (106, 2) = 1000.0, (107, 1) = 31.970843611055276, (107, 2) = 1000.0, (108, 1) = 32.25755536582914, (108, 2) = 1000.0, (109, 1) = 32.55442878090452, (109, 2) = 1000.0, (110, 1) = 32.86145569145728, (110, 2) = 1000.0, (111, 1) = 33.16749796281407, (111, 2) = 1000.0, (112, 1) = 33.4823000562814, (112, 2) = 1000.0, (113, 1) = 33.759577911557784, (113, 2) = 1000.0, (114, 1) = 34.07172710351758, (114, 2) = 1000.0, (115, 1) = 34.38515801005025, (115, 2) = 1000.0, (116, 1) = 34.687206765829146, (116, 2) = 1000.0, (117, 1) = 34.96149597286432, (117, 2) = 1000.0, (118, 1) = 35.28765236984924, (118, 2) = 1000.0, (119, 1) = 35.563949620100495, (119, 2) = 1000.0, (120, 1) = 35.88534900603015, (120, 2) = 1000.0, (121, 1) = 36.16984192160804, (121, 2) = 1000.0, (122, 1) = 36.48197573969849, (122, 2) = 1000.0, (123, 1) = 36.77920094773869, (123, 2) = 1000.0, (124, 1) = 37.08932427135678, (124, 2) = 1000.0, (125, 1) = 37.37411429246231, (125, 2) = 1000.0, (126, 1) = 37.6812988040201, (126, 2) = 1000.0, (127, 1) = 38.00037717889447, (127, 2) = 1000.0, (128, 1) = 38.27813584221106, (128, 2) = 1000.0, (129, 1) = 38.5781228080402, (129, 2) = 1000.0, (130, 1) = 38.88803869748743, (130, 2) = 1000.0, (131, 1) = 39.191230932663316, (131, 2) = 1000.0, (132, 1) = 39.484585010050246, (132, 2) = 1000.0, (133, 1) = 39.81030469748743, (133, 2) = 1000.0, (134, 1) = 40.10297832361809, (134, 2) = 1000.0, (135, 1) = 40.41546988944723, (135, 2) = 1000.0, (136, 1) = 40.69863369346733, (136, 2) = 1000.0, (137, 1) = 41.008206524623105, (137, 2) = 1000.0, (138, 1) = 41.29949043316583, (138, 2) = 1000.0, (139, 1) = 41.60396604723618, (139, 2) = 1000.0, (140, 1) = 41.90164661306532, (140, 2) = 1000.0, (141, 1) = 42.213290577889445, (141, 2) = 1000.0, (142, 1) = 42.51344075577889, (142, 2) = 1000.0, (143, 1) = 42.8203876643216, (143, 2) = 1000.0, (144, 1) = 43.12479289748743, (144, 2) = 1000.0, (145, 1) = 43.404509692462305, (145, 2) = 1000.0, (146, 1) = 43.72509670552763, (146, 2) = 1000.0, (147, 1) = 44.01183355175879, (147, 2) = 1000.0, (148, 1) = 44.31755483517587, (148, 2) = 1000.0, (149, 1) = 44.610169112562815, (149, 2) = 1000.0, (150, 1) = 44.93507966231155, (150, 2) = 1000.0, (151, 1) = 45.21642832462311, (151, 2) = 1000.0, (152, 1) = 45.53576157286432, (152, 2) = 1000.0, (153, 1) = 45.826799161809035, (153, 2) = 1000.0, (154, 1) = 46.14514854572864, (154, 2) = 1000.0, (155, 1) = 46.41983022512562, (155, 2) = 1000.0, (156, 1) = 46.73266059497487, (156, 2) = 1000.0, (157, 1) = 47.03483928844221, (157, 2) = 1000.0, (158, 1) = 47.33682057587939, (158, 2) = 1000.0, (159, 1) = 47.63769092864321, (159, 2) = 1000.0, (160, 1) = 47.92673314673367, (160, 2) = 1000.0, (161, 1) = 48.23919543919598, (161, 2) = 1000.0, (162, 1) = 48.5369946603015, (162, 2) = 1000.0, (163, 1) = 48.85041431758794, (163, 2) = 1000.0, (164, 1) = 49.134134580904515, (164, 2) = 1000.0, (165, 1) = 49.447698584924616, (165, 2) = 1000.0, (166, 1) = 49.748038260301506, (166, 2) = 1000.0, (167, 1) = 50.047646900502514, (167, 2) = 1000.0, (168, 1) = 50.36058928643215, (168, 2) = 1000.0, (169, 1) = 50.6488206482412, (169, 2) = 1000.0, (170, 1) = 50.94400898894472, (170, 2) = 1000.0, (171, 1) = 51.26993199195979, (171, 2) = 1000.0, (172, 1) = 51.56502857487437, (172, 2) = 1000.0, (173, 1) = 51.86682010552764, (173, 2) = 1000.0, (174, 1) = 52.17373431859296, (174, 2) = 1000.0, (175, 1) = 52.4558482040201, (175, 2) = 1000.0, (176, 1) = 52.756572470351756, (176, 2) = 1000.0, (177, 1) = 53.0550076040201, (177, 2) = 1000.0, (178, 1) = 53.374240432160796, (178, 2) = 1000.0, (179, 1) = 53.65594957386934, (179, 2) = 1000.0, (180, 1) = 53.980983443216076, (180, 2) = 1000.0, (181, 1) = 54.27430145125628, (181, 2) = 1000.0, (182, 1) = 54.56452428844221, (182, 2) = 1000.0, (183, 1) = 54.876607073366834, (183, 2) = 1000.0, (184, 1) = 55.18995229748743, (184, 2) = 1000.0, (185, 1) = 55.47505005527638, (185, 2) = 1000.0, (186, 1) = 55.777811210050245, (186, 2) = 1000.0, (187, 1) = 56.07327650653266, (187, 2) = 1000.0, (188, 1) = 56.39356400502512, (188, 2) = 1000.0, (189, 1) = 56.67070174070351, (189, 2) = 1000.0, (190, 1) = 56.98900450552763, (190, 2) = 1000.0, (191, 1) = 57.288225838190954, (191, 2) = 1000.0, (192, 1) = 57.58455701909548, (192, 2) = 1000.0, (193, 1) = 57.881123933668334, (193, 2) = 1000.0, (194, 1) = 58.18360341407034, (194, 2) = 1000.0, (195, 1) = 58.504226595979894, (195, 2) = 1000.0, (196, 1) = 58.79820665728643, (196, 2) = 1000.0, (197, 1) = 59.08840272663316, (197, 2) = 1000.0, (198, 1) = 59.398617548743715, (198, 2) = 1000.0, (199, 1) = 59.708157060301495, (199, 2) = 1000.0, (200, 1) = 60.0, (200, 2) = 1000.0}, datatype = float[8])), CURVES(Matrix(200, 2, {(1, 1) = .0, (1, 2) = 10000.0, (2, 1) = .3154563015075377, (2, 2) = 10000.0, (3, 1) = .5899331427135678, (3, 2) = 10000.0, (4, 1) = .8986110572864321, (4, 2) = 10000.0, (5, 1) = 1.2093350894472361, (5, 2) = 10000.0, (6, 1) = 1.5185823045226128, (6, 2) = 10000.0, (7, 1) = 1.8052940592964821, (7, 2) = 10000.0, (8, 1) = 2.102167474371859, (8, 2) = 10000.0, (9, 1) = 2.409194384924623, (9, 2) = 10000.0, (10, 1) = 2.7152366562814065, (10, 2) = 10000.0, (11, 1) = 3.0300387497487438, (11, 2) = 10000.0, (12, 1) = 3.3073166050251253, (12, 2) = 10000.0, (13, 1) = 3.6194657969849247, (13, 2) = 10000.0, (14, 1) = 3.9328967035175877, (14, 2) = 10000.0, (15, 1) = 4.234945459296482, (15, 2) = 10000.0, (16, 1) = 4.509234666331658, (16, 2) = 10000.0, (17, 1) = 4.835391063316583, (17, 2) = 10000.0, (18, 1) = 5.111688313567838, (18, 2) = 10000.0, (19, 1) = 5.433087699497487, (19, 2) = 10000.0, (20, 1) = 5.717580615075376, (20, 2) = 10000.0, (21, 1) = 6.029714433165829, (21, 2) = 10000.0, (22, 1) = 6.32693964120603, (22, 2) = 10000.0, (23, 1) = 6.63706296482412, (23, 2) = 10000.0, (24, 1) = 6.9218529859296485, (24, 2) = 10000.0, (25, 1) = 7.229037497487436, (25, 2) = 10000.0, (26, 1) = 7.548115872361809, (26, 2) = 10000.0, (27, 1) = 7.825874535678391, (27, 2) = 10000.0, (28, 1) = 8.125861501507536, (28, 2) = 10000.0, (29, 1) = 8.435777390954772, (29, 2) = 10000.0, (30, 1) = 8.738969626130652, (30, 2) = 10000.0, (31, 1) = 9.032323703517587, (31, 2) = 10000.0, (32, 1) = 9.358043390954773, (32, 2) = 10000.0, (33, 1) = 9.650717017085425, (33, 2) = 10000.0, (34, 1) = 9.963208582914572, (34, 2) = 10000.0, (35, 1) = 10.246372386934672, (35, 2) = 10000.0, (36, 1) = 10.555945218090452, (36, 2) = 10000.0, (37, 1) = 10.847229126633163, (37, 2) = 10000.0, (38, 1) = 11.151704740703517, (38, 2) = 10000.0, (39, 1) = 11.449385306532662, (39, 2) = 10000.0, (40, 1) = 11.761029271356783, (40, 2) = 10000.0, (41, 1) = 12.06117944924623, (41, 2) = 10000.0, (42, 1) = 12.368126357788944, (42, 2) = 10000.0, (43, 1) = 12.672531590954774, (43, 2) = 10000.0, (44, 1) = 12.952248385929648, (44, 2) = 10000.0, (45, 1) = 13.272835398994975, (45, 2) = 10000.0, (46, 1) = 13.55957224522613, (46, 2) = 10000.0, (47, 1) = 13.865293528643216, (47, 2) = 10000.0, (48, 1) = 14.157907806030149, (48, 2) = 10000.0, (49, 1) = 14.482818355778894, (49, 2) = 10000.0, (50, 1) = 14.76416701809045, (50, 2) = 10000.0, (51, 1) = 15.083500266331658, (51, 2) = 10000.0, (52, 1) = 15.374537855276381, (52, 2) = 10000.0, (53, 1) = 15.69288723919598, (53, 2) = 10000.0, (54, 1) = 15.967568918592962, (54, 2) = 10000.0, (55, 1) = 16.28039928844221, (55, 2) = 10000.0, (56, 1) = 16.582577981909548, (56, 2) = 10000.0, (57, 1) = 16.88455926934673, (57, 2) = 10000.0, (58, 1) = 17.18542962211055, (58, 2) = 10000.0, (59, 1) = 17.474471840201005, (59, 2) = 10000.0, (60, 1) = 17.786934132663315, (60, 2) = 10000.0, (61, 1) = 18.084733353768844, (61, 2) = 10000.0, (62, 1) = 18.398153011055275, (62, 2) = 10000.0, (63, 1) = 18.681873274371856, (63, 2) = 10000.0, (64, 1) = 18.995437278391957, (64, 2) = 10000.0, (65, 1) = 19.295776953768843, (65, 2) = 10000.0, (66, 1) = 19.595385593969848, (66, 2) = 10000.0, (67, 1) = 19.908327979899497, (67, 2) = 10000.0, (68, 1) = 20.19655934170854, (68, 2) = 10000.0, (69, 1) = 20.491747682412058, (69, 2) = 10000.0, (70, 1) = 20.817670685427135, (70, 2) = 10000.0, (71, 1) = 21.112767268341706, (71, 2) = 10000.0, (72, 1) = 21.414558798994975, (72, 2) = 10000.0, (73, 1) = 21.7214730120603, (73, 2) = 10000.0, (74, 1) = 22.003586897487438, (74, 2) = 10000.0, (75, 1) = 22.304311163819094, (75, 2) = 10000.0, (76, 1) = 22.602746297487435, (76, 2) = 10000.0, (77, 1) = 22.92197912562814, (77, 2) = 10000.0, (78, 1) = 23.20368826733668, (78, 2) = 10000.0, (79, 1) = 23.528722136683413, (79, 2) = 10000.0, (80, 1) = 23.822040144723616, (80, 2) = 10000.0, (81, 1) = 24.112262981909545, (81, 2) = 10000.0, (82, 1) = 24.42434576683417, (82, 2) = 10000.0, (83, 1) = 24.73769099095477, (83, 2) = 10000.0, (84, 1) = 25.022788748743714, (84, 2) = 10000.0, (85, 1) = 25.325549903517587, (85, 2) = 10000.0, (86, 1) = 25.6210152, (86, 2) = 10000.0, (87, 1) = 25.94130269849246, (87, 2) = 10000.0, (88, 1) = 26.21844043417085, (88, 2) = 10000.0, (89, 1) = 26.536743198994973, (89, 2) = 10000.0, (90, 1) = 26.835964531658288, (90, 2) = 10000.0, (91, 1) = 27.13229571256281, (91, 2) = 10000.0, (92, 1) = 27.428862627135675, (92, 2) = 10000.0, (93, 1) = 27.73134210753769, (93, 2) = 10000.0, (94, 1) = 28.05196528944723, (94, 2) = 10000.0, (95, 1) = 28.345945350753766, (95, 2) = 10000.0, (96, 1) = 28.636141420100497, (96, 2) = 10000.0, (97, 1) = 28.946356242211053, (97, 2) = 10000.0, (98, 1) = 29.255895753768844, (98, 2) = 10000.0, (99, 1) = 29.53372584723618, (99, 2) = 10000.0, (100, 1) = 29.862835628140704, (100, 2) = 10000.0, (101, 1) = 30.138219431155775, (101, 2) = 10000.0, (102, 1) = 30.46031172060301, (102, 2) = 10000.0, (103, 1) = 30.767717608040197, (103, 2) = 10000.0, (104, 1) = 31.042194449246228, (104, 2) = 10000.0, (105, 1) = 31.350872363819093, (105, 2) = 10000.0, (106, 1) = 31.661596395979895, (106, 2) = 10000.0, (107, 1) = 31.970843611055276, (107, 2) = 10000.0, (108, 1) = 32.25755536582914, (108, 2) = 10000.0, (109, 1) = 32.55442878090452, (109, 2) = 10000.0, (110, 1) = 32.86145569145728, (110, 2) = 10000.0, (111, 1) = 33.16749796281407, (111, 2) = 10000.0, (112, 1) = 33.4823000562814, (112, 2) = 10000.0, (113, 1) = 33.759577911557784, (113, 2) = 10000.0, (114, 1) = 34.07172710351758, (114, 2) = 10000.0, (115, 1) = 34.38515801005025, (115, 2) = 10000.0, (116, 1) = 34.687206765829146, (116, 2) = 10000.0, (117, 1) = 34.96149597286432, (117, 2) = 10000.0, (118, 1) = 35.28765236984924, (118, 2) = 10000.0, (119, 1) = 35.563949620100495, (119, 2) = 10000.0, (120, 1) = 35.88534900603015, (120, 2) = 10000.0, (121, 1) = 36.16984192160804, (121, 2) = 10000.0, (122, 1) = 36.48197573969849, (122, 2) = 10000.0, (123, 1) = 36.77920094773869, (123, 2) = 10000.0, (124, 1) = 37.08932427135678, (124, 2) = 10000.0, (125, 1) = 37.37411429246231, (125, 2) = 10000.0, (126, 1) = 37.6812988040201, (126, 2) = 10000.0, (127, 1) = 38.00037717889447, (127, 2) = 10000.0, (128, 1) = 38.27813584221106, (128, 2) = 10000.0, (129, 1) = 38.5781228080402, (129, 2) = 10000.0, (130, 1) = 38.88803869748743, (130, 2) = 10000.0, (131, 1) = 39.191230932663316, (131, 2) = 10000.0, (132, 1) = 39.484585010050246, (132, 2) = 10000.0, (133, 1) = 39.81030469748743, (133, 2) = 10000.0, (134, 1) = 40.10297832361809, (134, 2) = 10000.0, (135, 1) = 40.41546988944723, (135, 2) = 10000.0, (136, 1) = 40.69863369346733, (136, 2) = 10000.0, (137, 1) = 41.008206524623105, (137, 2) = 10000.0, (138, 1) = 41.29949043316583, (138, 2) = 10000.0, (139, 1) = 41.60396604723618, (139, 2) = 10000.0, (140, 1) = 41.90164661306532, (140, 2) = 10000.0, (141, 1) = 42.213290577889445, (141, 2) = 10000.0, (142, 1) = 42.51344075577889, (142, 2) = 10000.0, (143, 1) = 42.8203876643216, (143, 2) = 10000.0, (144, 1) = 43.12479289748743, (144, 2) = 10000.0, (145, 1) = 43.404509692462305, (145, 2) = 10000.0, (146, 1) = 43.72509670552763, (146, 2) = 10000.0, (147, 1) = 44.01183355175879, (147, 2) = 10000.0, (148, 1) = 44.31755483517587, (148, 2) = 10000.0, (149, 1) = 44.610169112562815, (149, 2) = 10000.0, (150, 1) = 44.93507966231155, (150, 2) = 10000.0, (151, 1) = 45.21642832462311, (151, 2) = 10000.0, (152, 1) = 45.53576157286432, (152, 2) = 10000.0, (153, 1) = 45.826799161809035, (153, 2) = 10000.0, (154, 1) = 46.14514854572864, (154, 2) = 10000.0, (155, 1) = 46.41983022512562, (155, 2) = 10000.0, (156, 1) = 46.73266059497487, (156, 2) = 10000.0, (157, 1) = 47.03483928844221, (157, 2) = 10000.0, (158, 1) = 47.33682057587939, (158, 2) = 10000.0, (159, 1) = 47.63769092864321, (159, 2) = 10000.0, (160, 1) = 47.92673314673367, (160, 2) = 10000.0, (161, 1) = 48.23919543919598, (161, 2) = 10000.0, (162, 1) = 48.5369946603015, (162, 2) = 10000.0, (163, 1) = 48.85041431758794, (163, 2) = 10000.0, (164, 1) = 49.134134580904515, (164, 2) = 10000.0, (165, 1) = 49.447698584924616, (165, 2) = 10000.0, (166, 1) = 49.748038260301506, (166, 2) = 10000.0, (167, 1) = 50.047646900502514, (167, 2) = 10000.0, (168, 1) = 50.36058928643215, (168, 2) = 10000.0, (169, 1) = 50.6488206482412, (169, 2) = 10000.0, (170, 1) = 50.94400898894472, (170, 2) = 10000.0, (171, 1) = 51.26993199195979, (171, 2) = 10000.0, (172, 1) = 51.56502857487437, (172, 2) = 10000.0, (173, 1) = 51.86682010552764, (173, 2) = 10000.0, (174, 1) = 52.17373431859296, (174, 2) = 10000.0, (175, 1) = 52.4558482040201, (175, 2) = 10000.0, (176, 1) = 52.756572470351756, (176, 2) = 10000.0, (177, 1) = 53.0550076040201, (177, 2) = 10000.0, (178, 1) = 53.374240432160796, (178, 2) = 10000.0, (179, 1) = 53.65594957386934, (179, 2) = 10000.0, (180, 1) = 53.980983443216076, (180, 2) = 10000.0, (181, 1) = 54.27430145125628, (181, 2) = 10000.0, (182, 1) = 54.56452428844221, (182, 2) = 10000.0, (183, 1) = 54.876607073366834, (183, 2) = 10000.0, (184, 1) = 55.18995229748743, (184, 2) = 10000.0, (185, 1) = 55.47505005527638, (185, 2) = 10000.0, (186, 1) = 55.777811210050245, (186, 2) = 10000.0, (187, 1) = 56.07327650653266, (187, 2) = 10000.0, (188, 1) = 56.39356400502512, (188, 2) = 10000.0, (189, 1) = 56.67070174070351, (189, 2) = 10000.0, (190, 1) = 56.98900450552763, (190, 2) = 10000.0, (191, 1) = 57.288225838190954, (191, 2) = 10000.0, (192, 1) = 57.58455701909548, (192, 2) = 10000.0, (193, 1) = 57.881123933668334, (193, 2) = 10000.0, (194, 1) = 58.18360341407034, (194, 2) = 10000.0, (195, 1) = 58.504226595979894, (195, 2) = 10000.0, (196, 1) = 58.79820665728643, (196, 2) = 10000.0, (197, 1) = 59.08840272663316, (197, 2) = 10000.0, (198, 1) = 59.398617548743715, (198, 2) = 10000.0, (199, 1) = 59.708157060301495, (199, 2) = 10000.0, (200, 1) = 60.0, (200, 2) = 10000.0}, datatype = float[8])), CURVES(Matrix(200, 2, {(1, 1) = .0, (1, 2) = 100000.0, (2, 1) = .3154563015075377, (2, 2) = 100000.0, (3, 1) = .5899331427135678, (3, 2) = 100000.0, (4, 1) = .8986110572864321, (4, 2) = 100000.0, (5, 1) = 1.2093350894472361, (5, 2) = 100000.0, (6, 1) = 1.5185823045226128, (6, 2) = 100000.0, (7, 1) = 1.8052940592964821, (7, 2) = 100000.0, (8, 1) = 2.102167474371859, (8, 2) = 100000.0, (9, 1) = 2.409194384924623, (9, 2) = 100000.0, (10, 1) = 2.7152366562814065, (10, 2) = 100000.0, (11, 1) = 3.0300387497487438, (11, 2) = 100000.0, (12, 1) = 3.3073166050251253, (12, 2) = 100000.0, (13, 1) = 3.6194657969849247, (13, 2) = 100000.0, (14, 1) = 3.9328967035175877, (14, 2) = 100000.0, (15, 1) = 4.234945459296482, (15, 2) = 100000.0, (16, 1) = 4.509234666331658, (16, 2) = 100000.0, (17, 1) = 4.835391063316583, (17, 2) = 100000.0, (18, 1) = 5.111688313567838, (18, 2) = 100000.0, (19, 1) = 5.433087699497487, (19, 2) = 100000.0, (20, 1) = 5.717580615075376, (20, 2) = 100000.0, (21, 1) = 6.029714433165829, (21, 2) = 100000.0, (22, 1) = 6.32693964120603, (22, 2) = 100000.0, (23, 1) = 6.63706296482412, (23, 2) = 100000.0, (24, 1) = 6.9218529859296485, (24, 2) = 100000.0, (25, 1) = 7.229037497487436, (25, 2) = 100000.0, (26, 1) = 7.548115872361809, (26, 2) = 100000.0, (27, 1) = 7.825874535678391, (27, 2) = 100000.0, (28, 1) = 8.125861501507536, (28, 2) = 100000.0, (29, 1) = 8.435777390954772, (29, 2) = 100000.0, (30, 1) = 8.738969626130652, (30, 2) = 100000.0, (31, 1) = 9.032323703517587, (31, 2) = 100000.0, (32, 1) = 9.358043390954773, (32, 2) = 100000.0, (33, 1) = 9.650717017085425, (33, 2) = 100000.0, (34, 1) = 9.963208582914572, (34, 2) = 100000.0, (35, 1) = 10.246372386934672, (35, 2) = 100000.0, (36, 1) = 10.555945218090452, (36, 2) = 100000.0, (37, 1) = 10.847229126633163, (37, 2) = 100000.0, (38, 1) = 11.151704740703517, (38, 2) = 100000.0, (39, 1) = 11.449385306532662, (39, 2) = 100000.0, (40, 1) = 11.761029271356783, (40, 2) = 100000.0, (41, 1) = 12.06117944924623, (41, 2) = 100000.0, (42, 1) = 12.368126357788944, (42, 2) = 100000.0, (43, 1) = 12.672531590954774, (43, 2) = 100000.0, (44, 1) = 12.952248385929648, (44, 2) = 100000.0, (45, 1) = 13.272835398994975, (45, 2) = 100000.0, (46, 1) = 13.55957224522613, (46, 2) = 100000.0, (47, 1) = 13.865293528643216, (47, 2) = 100000.0, (48, 1) = 14.157907806030149, (48, 2) = 100000.0, (49, 1) = 14.482818355778894, (49, 2) = 100000.0, (50, 1) = 14.76416701809045, (50, 2) = 100000.0, (51, 1) = 15.083500266331658, (51, 2) = 100000.0, (52, 1) = 15.374537855276381, (52, 2) = 100000.0, (53, 1) = 15.69288723919598, (53, 2) = 100000.0, (54, 1) = 15.967568918592962, (54, 2) = 100000.0, (55, 1) = 16.28039928844221, (55, 2) = 100000.0, (56, 1) = 16.582577981909548, (56, 2) = 100000.0, (57, 1) = 16.88455926934673, (57, 2) = 100000.0, (58, 1) = 17.18542962211055, (58, 2) = 100000.0, (59, 1) = 17.474471840201005, (59, 2) = 100000.0, (60, 1) = 17.786934132663315, (60, 2) = 100000.0, (61, 1) = 18.084733353768844, (61, 2) = 100000.0, (62, 1) = 18.398153011055275, (62, 2) = 100000.0, (63, 1) = 18.681873274371856, (63, 2) = 100000.0, (64, 1) = 18.995437278391957, (64, 2) = 100000.0, (65, 1) = 19.295776953768843, (65, 2) = 100000.0, (66, 1) = 19.595385593969848, (66, 2) = 100000.0, (67, 1) = 19.908327979899497, (67, 2) = 100000.0, (68, 1) = 20.19655934170854, (68, 2) = 100000.0, (69, 1) = 20.491747682412058, (69, 2) = 100000.0, (70, 1) = 20.817670685427135, (70, 2) = 100000.0, (71, 1) = 21.112767268341706, (71, 2) = 100000.0, (72, 1) = 21.414558798994975, (72, 2) = 100000.0, (73, 1) = 21.7214730120603, (73, 2) = 100000.0, (74, 1) = 22.003586897487438, (74, 2) = 100000.0, (75, 1) = 22.304311163819094, (75, 2) = 100000.0, (76, 1) = 22.602746297487435, (76, 2) = 100000.0, (77, 1) = 22.92197912562814, (77, 2) = 100000.0, (78, 1) = 23.20368826733668, (78, 2) = 100000.0, (79, 1) = 23.528722136683413, (79, 2) = 100000.0, (80, 1) = 23.822040144723616, (80, 2) = 100000.0, (81, 1) = 24.112262981909545, (81, 2) = 100000.0, (82, 1) = 24.42434576683417, (82, 2) = 100000.0, (83, 1) = 24.73769099095477, (83, 2) = 100000.0, (84, 1) = 25.022788748743714, (84, 2) = 100000.0, (85, 1) = 25.325549903517587, (85, 2) = 100000.0, (86, 1) = 25.6210152, (86, 2) = 100000.0, (87, 1) = 25.94130269849246, (87, 2) = 100000.0, (88, 1) = 26.21844043417085, (88, 2) = 100000.0, (89, 1) = 26.536743198994973, (89, 2) = 100000.0, (90, 1) = 26.835964531658288, (90, 2) = 100000.0, (91, 1) = 27.13229571256281, (91, 2) = 100000.0, (92, 1) = 27.428862627135675, (92, 2) = 100000.0, (93, 1) = 27.73134210753769, (93, 2) = 100000.0, (94, 1) = 28.05196528944723, (94, 2) = 100000.0, (95, 1) = 28.345945350753766, (95, 2) = 100000.0, (96, 1) = 28.636141420100497, (96, 2) = 100000.0, (97, 1) = 28.946356242211053, (97, 2) = 100000.0, (98, 1) = 29.255895753768844, (98, 2) = 100000.0, (99, 1) = 29.53372584723618, (99, 2) = 100000.0, (100, 1) = 29.862835628140704, (100, 2) = 100000.0, (101, 1) = 30.138219431155775, (101, 2) = 100000.0, (102, 1) = 30.46031172060301, (102, 2) = 100000.0, (103, 1) = 30.767717608040197, (103, 2) = 100000.0, (104, 1) = 31.042194449246228, (104, 2) = 100000.0, (105, 1) = 31.350872363819093, (105, 2) = 100000.0, (106, 1) = 31.661596395979895, (106, 2) = 100000.0, (107, 1) = 31.970843611055276, (107, 2) = 100000.0, (108, 1) = 32.25755536582914, (108, 2) = 100000.0, (109, 1) = 32.55442878090452, (109, 2) = 100000.0, (110, 1) = 32.86145569145728, (110, 2) = 100000.0, (111, 1) = 33.16749796281407, (111, 2) = 100000.0, (112, 1) = 33.4823000562814, (112, 2) = 100000.0, (113, 1) = 33.759577911557784, (113, 2) = 100000.0, (114, 1) = 34.07172710351758, (114, 2) = 100000.0, (115, 1) = 34.38515801005025, (115, 2) = 100000.0, (116, 1) = 34.687206765829146, (116, 2) = 100000.0, (117, 1) = 34.96149597286432, (117, 2) = 100000.0, (118, 1) = 35.28765236984924, (118, 2) = 100000.0, (119, 1) = 35.563949620100495, (119, 2) = 100000.0, (120, 1) = 35.88534900603015, (120, 2) = 100000.0, (121, 1) = 36.16984192160804, (121, 2) = 100000.0, (122, 1) = 36.48197573969849, (122, 2) = 100000.0, (123, 1) = 36.77920094773869, (123, 2) = 100000.0, (124, 1) = 37.08932427135678, (124, 2) = 100000.0, (125, 1) = 37.37411429246231, (125, 2) = 100000.0, (126, 1) = 37.6812988040201, (126, 2) = 100000.0, (127, 1) = 38.00037717889447, (127, 2) = 100000.0, (128, 1) = 38.27813584221106, (128, 2) = 100000.0, (129, 1) = 38.5781228080402, (129, 2) = 100000.0, (130, 1) = 38.88803869748743, (130, 2) = 100000.0, (131, 1) = 39.191230932663316, (131, 2) = 100000.0, (132, 1) = 39.484585010050246, (132, 2) = 100000.0, (133, 1) = 39.81030469748743, (133, 2) = 100000.0, (134, 1) = 40.10297832361809, (134, 2) = 100000.0, (135, 1) = 40.41546988944723, (135, 2) = 100000.0, (136, 1) = 40.69863369346733, (136, 2) = 100000.0, (137, 1) = 41.008206524623105, (137, 2) = 100000.0, (138, 1) = 41.29949043316583, (138, 2) = 100000.0, (139, 1) = 41.60396604723618, (139, 2) = 100000.0, (140, 1) = 41.90164661306532, (140, 2) = 100000.0, (141, 1) = 42.213290577889445, (141, 2) = 100000.0, (142, 1) = 42.51344075577889, (142, 2) = 100000.0, (143, 1) = 42.8203876643216, (143, 2) = 100000.0, (144, 1) = 43.12479289748743, (144, 2) = 100000.0, (145, 1) = 43.404509692462305, (145, 2) = 100000.0, (146, 1) = 43.72509670552763, (146, 2) = 100000.0, (147, 1) = 44.01183355175879, (147, 2) = 100000.0, (148, 1) = 44.31755483517587, (148, 2) = 100000.0, (149, 1) = 44.610169112562815, (149, 2) = 100000.0, (150, 1) = 44.93507966231155, (150, 2) = 100000.0, (151, 1) = 45.21642832462311, (151, 2) = 100000.0, (152, 1) = 45.53576157286432, (152, 2) = 100000.0, (153, 1) = 45.826799161809035, (153, 2) = 100000.0, (154, 1) = 46.14514854572864, (154, 2) = 100000.0, (155, 1) = 46.41983022512562, (155, 2) = 100000.0, (156, 1) = 46.73266059497487, (156, 2) = 100000.0, (157, 1) = 47.03483928844221, (157, 2) = 100000.0, (158, 1) = 47.33682057587939, (158, 2) = 100000.0, (159, 1) = 47.63769092864321, (159, 2) = 100000.0, (160, 1) = 47.92673314673367, (160, 2) = 100000.0, (161, 1) = 48.23919543919598, (161, 2) = 100000.0, (162, 1) = 48.5369946603015, (162, 2) = 100000.0, (163, 1) = 48.85041431758794, (163, 2) = 100000.0, (164, 1) = 49.134134580904515, (164, 2) = 100000.0, (165, 1) = 49.447698584924616, (165, 2) = 100000.0, (166, 1) = 49.748038260301506, (166, 2) = 100000.0, (167, 1) = 50.047646900502514, (167, 2) = 100000.0, (168, 1) = 50.36058928643215, (168, 2) = 100000.0, (169, 1) = 50.6488206482412, (169, 2) = 100000.0, (170, 1) = 50.94400898894472, (170, 2) = 100000.0, (171, 1) = 51.26993199195979, (171, 2) = 100000.0, (172, 1) = 51.56502857487437, (172, 2) = 100000.0, (173, 1) = 51.86682010552764, (173, 2) = 100000.0, (174, 1) = 52.17373431859296, (174, 2) = 100000.0, (175, 1) = 52.4558482040201, (175, 2) = 100000.0, (176, 1) = 52.756572470351756, (176, 2) = 100000.0, (177, 1) = 53.0550076040201, (177, 2) = 100000.0, (178, 1) = 53.374240432160796, (178, 2) = 100000.0, (179, 1) = 53.65594957386934, (179, 2) = 100000.0, (180, 1) = 53.980983443216076, (180, 2) = 100000.0, (181, 1) = 54.27430145125628, (181, 2) = 100000.0, (182, 1) = 54.56452428844221, (182, 2) = 100000.0, (183, 1) = 54.876607073366834, (183, 2) = 100000.0, (184, 1) = 55.18995229748743, (184, 2) = 100000.0, (185, 1) = 55.47505005527638, (185, 2) = 100000.0, (186, 1) = 55.777811210050245, (186, 2) = 100000.0, (187, 1) = 56.07327650653266, (187, 2) = 100000.0, (188, 1) = 56.39356400502512, (188, 2) = 100000.0, (189, 1) = 56.67070174070351, (189, 2) = 100000.0, (190, 1) = 56.98900450552763, (190, 2) = 100000.0, (191, 1) = 57.288225838190954, (191, 2) = 100000.0, (192, 1) = 57.58455701909548, (192, 2) = 100000.0, (193, 1) = 57.881123933668334, (193, 2) = 100000.0, (194, 1) = 58.18360341407034, (194, 2) = 100000.0, (195, 1) = 58.504226595979894, (195, 2) = 100000.0, (196, 1) = 58.79820665728643, (196, 2) = 100000.0, (197, 1) = 59.08840272663316, (197, 2) = 100000.0, (198, 1) = 59.398617548743715, (198, 2) = 100000.0, (199, 1) = 59.708157060301495, (199, 2) = 100000.0, (200, 1) = 60.0, (200, 2) = 100000.0}, datatype = float[8])), CURVES(Matrix(200, 2, {(1, 1) = .0, (1, 2) = 1000000.0, (2, 1) = .3154563015075377, (2, 2) = 1000000.0, (3, 1) = .5899331427135678, (3, 2) = 1000000.0, (4, 1) = .8986110572864321, (4, 2) = 1000000.0, (5, 1) = 1.2093350894472361, (5, 2) = 1000000.0, (6, 1) = 1.5185823045226128, (6, 2) = 1000000.0, (7, 1) = 1.8052940592964821, (7, 2) = 1000000.0, (8, 1) = 2.102167474371859, (8, 2) = 1000000.0, (9, 1) = 2.409194384924623, (9, 2) = 1000000.0, (10, 1) = 2.7152366562814065, (10, 2) = 1000000.0, (11, 1) = 3.0300387497487438, (11, 2) = 1000000.0, (12, 1) = 3.3073166050251253, (12, 2) = 1000000.0, (13, 1) = 3.6194657969849247, (13, 2) = 1000000.0, (14, 1) = 3.9328967035175877, (14, 2) = 1000000.0, (15, 1) = 4.234945459296482, (15, 2) = 1000000.0, (16, 1) = 4.509234666331658, (16, 2) = 1000000.0, (17, 1) = 4.835391063316583, (17, 2) = 1000000.0, (18, 1) = 5.111688313567838, (18, 2) = 1000000.0, (19, 1) = 5.433087699497487, (19, 2) = 1000000.0, (20, 1) = 5.717580615075376, (20, 2) = 1000000.0, (21, 1) = 6.029714433165829, (21, 2) = 1000000.0, (22, 1) = 6.32693964120603, (22, 2) = 1000000.0, (23, 1) = 6.63706296482412, (23, 2) = 1000000.0, (24, 1) = 6.9218529859296485, (24, 2) = 1000000.0, (25, 1) = 7.229037497487436, (25, 2) = 1000000.0, (26, 1) = 7.548115872361809, (26, 2) = 1000000.0, (27, 1) = 7.825874535678391, (27, 2) = 1000000.0, (28, 1) = 8.125861501507536, (28, 2) = 1000000.0, (29, 1) = 8.435777390954772, (29, 2) = 1000000.0, (30, 1) = 8.738969626130652, (30, 2) = 1000000.0, (31, 1) = 9.032323703517587, (31, 2) = 1000000.0, (32, 1) = 9.358043390954773, (32, 2) = 1000000.0, (33, 1) = 9.650717017085425, (33, 2) = 1000000.0, (34, 1) = 9.963208582914572, (34, 2) = 1000000.0, (35, 1) = 10.246372386934672, (35, 2) = 1000000.0, (36, 1) = 10.555945218090452, (36, 2) = 1000000.0, (37, 1) = 10.847229126633163, (37, 2) = 1000000.0, (38, 1) = 11.151704740703517, (38, 2) = 1000000.0, (39, 1) = 11.449385306532662, (39, 2) = 1000000.0, (40, 1) = 11.761029271356783, (40, 2) = 1000000.0, (41, 1) = 12.06117944924623, (41, 2) = 1000000.0, (42, 1) = 12.368126357788944, (42, 2) = 1000000.0, (43, 1) = 12.672531590954774, (43, 2) = 1000000.0, (44, 1) = 12.952248385929648, (44, 2) = 1000000.0, (45, 1) = 13.272835398994975, (45, 2) = 1000000.0, (46, 1) = 13.55957224522613, (46, 2) = 1000000.0, (47, 1) = 13.865293528643216, (47, 2) = 1000000.0, (48, 1) = 14.157907806030149, (48, 2) = 1000000.0, (49, 1) = 14.482818355778894, (49, 2) = 1000000.0, (50, 1) = 14.76416701809045, (50, 2) = 1000000.0, (51, 1) = 15.083500266331658, (51, 2) = 1000000.0, (52, 1) = 15.374537855276381, (52, 2) = 1000000.0, (53, 1) = 15.69288723919598, (53, 2) = 1000000.0, (54, 1) = 15.967568918592962, (54, 2) = 1000000.0, (55, 1) = 16.28039928844221, (55, 2) = 1000000.0, (56, 1) = 16.582577981909548, (56, 2) = 1000000.0, (57, 1) = 16.88455926934673, (57, 2) = 1000000.0, (58, 1) = 17.18542962211055, (58, 2) = 1000000.0, (59, 1) = 17.474471840201005, (59, 2) = 1000000.0, (60, 1) = 17.786934132663315, (60, 2) = 1000000.0, (61, 1) = 18.084733353768844, (61, 2) = 1000000.0, (62, 1) = 18.398153011055275, (62, 2) = 1000000.0, (63, 1) = 18.681873274371856, (63, 2) = 1000000.0, (64, 1) = 18.995437278391957, (64, 2) = 1000000.0, (65, 1) = 19.295776953768843, (65, 2) = 1000000.0, (66, 1) = 19.595385593969848, (66, 2) = 1000000.0, (67, 1) = 19.908327979899497, (67, 2) = 1000000.0, (68, 1) = 20.19655934170854, (68, 2) = 1000000.0, (69, 1) = 20.491747682412058, (69, 2) = 1000000.0, (70, 1) = 20.817670685427135, (70, 2) = 1000000.0, (71, 1) = 21.112767268341706, (71, 2) = 1000000.0, (72, 1) = 21.414558798994975, (72, 2) = 1000000.0, (73, 1) = 21.7214730120603, (73, 2) = 1000000.0, (74, 1) = 22.003586897487438, (74, 2) = 1000000.0, (75, 1) = 22.304311163819094, (75, 2) = 1000000.0, (76, 1) = 22.602746297487435, (76, 2) = 1000000.0, (77, 1) = 22.92197912562814, (77, 2) = 1000000.0, (78, 1) = 23.20368826733668, (78, 2) = 1000000.0, (79, 1) = 23.528722136683413, (79, 2) = 1000000.0, (80, 1) = 23.822040144723616, (80, 2) = 1000000.0, (81, 1) = 24.112262981909545, (81, 2) = 1000000.0, (82, 1) = 24.42434576683417, (82, 2) = 1000000.0, (83, 1) = 24.73769099095477, (83, 2) = 1000000.0, (84, 1) = 25.022788748743714, (84, 2) = 1000000.0, (85, 1) = 25.325549903517587, (85, 2) = 1000000.0, (86, 1) = 25.6210152, (86, 2) = 1000000.0, (87, 1) = 25.94130269849246, (87, 2) = 1000000.0, (88, 1) = 26.21844043417085, (88, 2) = 1000000.0, (89, 1) = 26.536743198994973, (89, 2) = 1000000.0, (90, 1) = 26.835964531658288, (90, 2) = 1000000.0, (91, 1) = 27.13229571256281, (91, 2) = 1000000.0, (92, 1) = 27.428862627135675, (92, 2) = 1000000.0, (93, 1) = 27.73134210753769, (93, 2) = 1000000.0, (94, 1) = 28.05196528944723, (94, 2) = 1000000.0, (95, 1) = 28.345945350753766, (95, 2) = 1000000.0, (96, 1) = 28.636141420100497, (96, 2) = 1000000.0, (97, 1) = 28.946356242211053, (97, 2) = 1000000.0, (98, 1) = 29.255895753768844, (98, 2) = 1000000.0, (99, 1) = 29.53372584723618, (99, 2) = 1000000.0, (100, 1) = 29.862835628140704, (100, 2) = 1000000.0, (101, 1) = 30.138219431155775, (101, 2) = 1000000.0, (102, 1) = 30.46031172060301, (102, 2) = 1000000.0, (103, 1) = 30.767717608040197, (103, 2) = 1000000.0, (104, 1) = 31.042194449246228, (104, 2) = 1000000.0, (105, 1) = 31.350872363819093, (105, 2) = 1000000.0, (106, 1) = 31.661596395979895, (106, 2) = 1000000.0, (107, 1) = 31.970843611055276, (107, 2) = 1000000.0, (108, 1) = 32.25755536582914, (108, 2) = 1000000.0, (109, 1) = 32.55442878090452, (109, 2) = 1000000.0, (110, 1) = 32.86145569145728, (110, 2) = 1000000.0, (111, 1) = 33.16749796281407, (111, 2) = 1000000.0, (112, 1) = 33.4823000562814, (112, 2) = 1000000.0, (113, 1) = 33.759577911557784, (113, 2) = 1000000.0, (114, 1) = 34.07172710351758, (114, 2) = 1000000.0, (115, 1) = 34.38515801005025, (115, 2) = 1000000.0, (116, 1) = 34.687206765829146, (116, 2) = 1000000.0, (117, 1) = 34.96149597286432, (117, 2) = 1000000.0, (118, 1) = 35.28765236984924, (118, 2) = 1000000.0, (119, 1) = 35.563949620100495, (119, 2) = 1000000.0, (120, 1) = 35.88534900603015, (120, 2) = 1000000.0, (121, 1) = 36.16984192160804, (121, 2) = 1000000.0, (122, 1) = 36.48197573969849, (122, 2) = 1000000.0, (123, 1) = 36.77920094773869, (123, 2) = 1000000.0, (124, 1) = 37.08932427135678, (124, 2) = 1000000.0, (125, 1) = 37.37411429246231, (125, 2) = 1000000.0, (126, 1) = 37.6812988040201, (126, 2) = 1000000.0, (127, 1) = 38.00037717889447, (127, 2) = 1000000.0, (128, 1) = 38.27813584221106, (128, 2) = 1000000.0, (129, 1) = 38.5781228080402, (129, 2) = 1000000.0, (130, 1) = 38.88803869748743, (130, 2) = 1000000.0, (131, 1) = 39.191230932663316, (131, 2) = 1000000.0, (132, 1) = 39.484585010050246, (132, 2) = 1000000.0, (133, 1) = 39.81030469748743, (133, 2) = 1000000.0, (134, 1) = 40.10297832361809, (134, 2) = 1000000.0, (135, 1) = 40.41546988944723, (135, 2) = 1000000.0, (136, 1) = 40.69863369346733, (136, 2) = 1000000.0, (137, 1) = 41.008206524623105, (137, 2) = 1000000.0, (138, 1) = 41.29949043316583, (138, 2) = 1000000.0, (139, 1) = 41.60396604723618, (139, 2) = 1000000.0, (140, 1) = 41.90164661306532, (140, 2) = 1000000.0, (141, 1) = 42.213290577889445, (141, 2) = 1000000.0, (142, 1) = 42.51344075577889, (142, 2) = 1000000.0, (143, 1) = 42.8203876643216, (143, 2) = 1000000.0, (144, 1) = 43.12479289748743, (144, 2) = 1000000.0, (145, 1) = 43.404509692462305, (145, 2) = 1000000.0, (146, 1) = 43.72509670552763, (146, 2) = 1000000.0, (147, 1) = 44.01183355175879, (147, 2) = 1000000.0, (148, 1) = 44.31755483517587, (148, 2) = 1000000.0, (149, 1) = 44.610169112562815, (149, 2) = 1000000.0, (150, 1) = 44.93507966231155, (150, 2) = 1000000.0, (151, 1) = 45.21642832462311, (151, 2) = 1000000.0, (152, 1) = 45.53576157286432, (152, 2) = 1000000.0, (153, 1) = 45.826799161809035, (153, 2) = 1000000.0, (154, 1) = 46.14514854572864, (154, 2) = 1000000.0, (155, 1) = 46.41983022512562, (155, 2) = 1000000.0, (156, 1) = 46.73266059497487, (156, 2) = 1000000.0, (157, 1) = 47.03483928844221, (157, 2) = 1000000.0, (158, 1) = 47.33682057587939, (158, 2) = 1000000.0, (159, 1) = 47.63769092864321, (159, 2) = 1000000.0, (160, 1) = 47.92673314673367, (160, 2) = 1000000.0, (161, 1) = 48.23919543919598, (161, 2) = 1000000.0, (162, 1) = 48.5369946603015, (162, 2) = 1000000.0, (163, 1) = 48.85041431758794, (163, 2) = 1000000.0, (164, 1) = 49.134134580904515, (164, 2) = 1000000.0, (165, 1) = 49.447698584924616, (165, 2) = 1000000.0, (166, 1) = 49.748038260301506, (166, 2) = 1000000.0, (167, 1) = 50.047646900502514, (167, 2) = 1000000.0, (168, 1) = 50.36058928643215, (168, 2) = 1000000.0, (169, 1) = 50.6488206482412, (169, 2) = 1000000.0, (170, 1) = 50.94400898894472, (170, 2) = 1000000.0, (171, 1) = 51.26993199195979, (171, 2) = 1000000.0, (172, 1) = 51.56502857487437, (172, 2) = 1000000.0, (173, 1) = 51.86682010552764, (173, 2) = 1000000.0, (174, 1) = 52.17373431859296, (174, 2) = 1000000.0, (175, 1) = 52.4558482040201, (175, 2) = 1000000.0, (176, 1) = 52.756572470351756, (176, 2) = 1000000.0, (177, 1) = 53.0550076040201, (177, 2) = 1000000.0, (178, 1) = 53.374240432160796, (178, 2) = 1000000.0, (179, 1) = 53.65594957386934, (179, 2) = 1000000.0, (180, 1) = 53.980983443216076, (180, 2) = 1000000.0, (181, 1) = 54.27430145125628, (181, 2) = 1000000.0, (182, 1) = 54.56452428844221, (182, 2) = 1000000.0, (183, 1) = 54.876607073366834, (183, 2) = 1000000.0, (184, 1) = 55.18995229748743, (184, 2) = 1000000.0, (185, 1) = 55.47505005527638, (185, 2) = 1000000.0, (186, 1) = 55.777811210050245, (186, 2) = 1000000.0, (187, 1) = 56.07327650653266, (187, 2) = 1000000.0, (188, 1) = 56.39356400502512, (188, 2) = 1000000.0, (189, 1) = 56.67070174070351, (189, 2) = 1000000.0, (190, 1) = 56.98900450552763, (190, 2) = 1000000.0, (191, 1) = 57.288225838190954, (191, 2) = 1000000.0, (192, 1) = 57.58455701909548, (192, 2) = 1000000.0, (193, 1) = 57.881123933668334, (193, 2) = 1000000.0, (194, 1) = 58.18360341407034, (194, 2) = 1000000.0, (195, 1) = 58.504226595979894, (195, 2) = 1000000.0, (196, 1) = 58.79820665728643, (196, 2) = 1000000.0, (197, 1) = 59.08840272663316, (197, 2) = 1000000.0, (198, 1) = 59.398617548743715, (198, 2) = 1000000.0, (199, 1) = 59.708157060301495, (199, 2) = 1000000.0, (200, 1) = 60.0, (200, 2) = 1000000.0}, datatype = float[8])), COLOUR(RGB, .90196078, .90196078, .90196078), THICKNESS(0), AXESLABELS(x, ""), VIEW(0. .. 60., DEFAULT, _ATTRIBUTE("source" = "mathdefault")))

    (5)

    plots:-display(a2, b2, title = "Total Deaths \n (Logarithmic scale)\n", titlefont = ["Helvetica", 18], size = [681, 400])

     

    One still could think and interpret that graph at levelling off to maybe 100,000.  I sense another Dr. Fauci prediction?  

    Let's take a look at the linear graph

     

    a3 := plots:-listplot(USTotalDeaths[32 .. ()], tickmarks = [[seq(i-31 = USTotaldeathsdates[i], i = 32 .. nops(USTotaldeathsdates))], [20000 = "20K", 40000 = "40K", 60000 = "60K", 80000 = "80K"]], view = [default, 100 .. 80000], color = "#FF9900", thickness = 6, labels = ["", "Total Coronavirus Deaths"], labeldirections = [default, vertical])

    PLOT(CURVES(Matrix(46, 2, {(1, 1) = 1.0, (1, 2) = 121.0, (2, 1) = 2.0, (2, 2) = 171.0, (3, 1) = 3.0, (3, 2) = 239.0, (4, 1) = 4.0, (4, 2) = 309.0, (5, 1) = 5.0, (5, 2) = 374.0, (6, 1) = 6.0, (6, 2) = 509.0, (7, 1) = 7.0, (7, 2) = 689.0, (8, 1) = 8.0, (8, 2) = 957.0, (9, 1) = 9.0, (9, 2) = 1260.0, (10, 1) = 10.0, (10, 2) = 1614.0, (11, 1) = 11.0, (11, 2) = 2110.0, (12, 1) = 12.0, (12, 2) = 2754.0, (13, 1) = 13.0, (13, 2) = 3251.0, (14, 1) = 14.0, (14, 2) = 4066.0, (15, 1) = 15.0, (15, 2) = 5151.0, (16, 1) = 16.0, (16, 2) = 6394.0, (17, 1) = 17.0, (17, 2) = 7576.0, (18, 1) = 18.0, (18, 2) = 8839.0, (19, 1) = 19.0, (19, 2) = 10384.0, (20, 1) = 20.0, (20, 2) = 11793.0, (21, 1) = 21.0, (21, 2) = 13298.0, (22, 1) = 22.0, (22, 2) = 15526.0, (23, 1) = 23.0, (23, 2) = 17691.0, (24, 1) = 24.0, (24, 2) = 19802.0, (25, 1) = 25.0, (25, 2) = 22038.0, (26, 1) = 26.0, (26, 2) = 24062.0, (27, 1) = 27.0, (27, 2) = 25789.0, (28, 1) = 28.0, (28, 2) = 27515.0, (29, 1) = 29.0, (29, 2) = 30081.0, (30, 1) = 30.0, (30, 2) = 32712.0, (31, 1) = 31.0, (31, 2) = 34905.0, (32, 1) = 32.0, (32, 2) = 37448.0, (33, 1) = 33.0, (33, 2) = 39331.0, (34, 1) = 34.0, (34, 2) = 40901.0, (35, 1) = 35.0, (35, 2) = 42853.0, (36, 1) = 36.0, (36, 2) = 45536.0, (37, 1) = 37.0, (37, 2) = 47894.0, (38, 1) = 38.0, (38, 2) = 50234.0, (39, 1) = 39.0, (39, 2) = 52191.0, (40, 1) = 40.0, (40, 2) = 54256.0, (41, 1) = 41.0, (41, 2) = 55412.0, (42, 1) = 42.0, (42, 2) = 56795.0, (43, 1) = 43.0, (43, 2) = 59265.0, (44, 1) = 44.0, (44, 2) = 61655.0, (45, 1) = 45.0, (45, 2) = 63856.0, (46, 1) = 46.0, (46, 2) = 65753.0}, datatype = float[8])), COLOUR(RGB, 1.00000000, .60000000, 0.), THICKNESS(6), AXESTICKS([1 = "Mar 17", 2 = "Mar 18", 3 = "Mar 19", 4 = "Mar 20", 5 = "Mar 21", 6 = "Mar 22", 7 = "Mar 23", 8 = "Mar 24", 9 = "Mar 25", 10 = "Mar 26", 11 = "Mar 27", 12 = "Mar 28", 13 = "Mar 29", 14 = "Mar 30", 15 = "Mar 31", 16 = "Apr 01", 17 = "Apr 02", 18 = "Apr 03", 19 = "Apr 04", 20 = "Apr 05", 21 = "Apr 06", 22 = "Apr 07", 23 = "Apr 08", 24 = "Apr 09", 25 = "Apr 10", 26 = "Apr 11", 27 = "Apr 12", 28 = "Apr 13", 29 = "Apr 14", 30 = "Apr 15", 31 = "Apr 16", 32 = "Apr 17", 33 = "Apr 18", 34 = "Apr 19", 35 = "Apr 20", 36 = "Apr 21", 37 = "Apr 22", 38 = "Apr 23", 39 = "Apr 24", 40 = "Apr 25", 41 = "Apr 26", 42 = "Apr 27", 43 = "Apr 28", 44 = "Apr 29", 45 = "Apr 30", 46 = "May 01"], [20000 = "20K", 40000 = "40K", 60000 = "60K", 80000 = "80K"]), AXESLABELS("", "Total Coronavirus Deaths", FONT(DEFAULT), DEFAULT, VERTICAL), VIEW(DEFAULT, 100 .. 80000))

    (6)

    b3 := plot([20000, 40000, 60000, 80000], x = 0 .. 60, color = "#E6E6E6", thickness = 0)