Suppose we have a 200-litre tank. Suppose 10 litres per minute of salt water (brine) flows into the tank at the top, it mixes perfectly with the contents of the tank, and 10 litres per minute of the mixture flows out of the tank at the bottom. Assume for simplicity that the salt water in the tank is stirred so that its concentration is uniform in the tank. Let S(t) be the amount of salt, in grams, in the tank at t time minutes. Suppose the salt water flowing into the tank has concentration 80 grams per litre.
Find the differential equation to model the change in S(t).
Assuming that at t = 0 time the concentration of salt in the tank is 10 grams per litre, solve the differential equation using Maple.
What is S(infinite)? That is, how much salt is in the tank after a long time?
Now graph S(t) for a suitable domain so we can see the function approaching the value S(infinite)
Have some difficulty to understand the problem. I mean, such modelling problem rather than pure math computation.
Thank you so much!