# Question:Differential Question pt. 3

## Question:Differential Question pt. 3

Im just on my last two questions and was wondering if you could help me again =D

So as a background to my question:

Show that dV/dt = -k * V^(2/3) given that k = 0.4836 and t is measured in minutes if the original volume of the capsule is 300 ml, how long will it take the capsule to lose half its volume?

Im doing this on maple right now and see you if guys can spot my problem or my syntax:
1. eq1 := diff(y(t), t) = -k*y(t)^(2/3)
2. dsolve(eq1, y(t)) which gives me an equation
3. dsolve({eq1, y(0) = 300}, y(t)) here i set the equation to equal to 300 to find my C
4. solve(subs(k = .4836, Y(t)), t) here i tried finding the time needed to lose half its volume but its giving me a set of numbers

So with oliver's help i was able to understand my syntax problems =D now on part 2:

Assuming the same size capsule as in question 2, suppose that the change in volume of the second capsule were instead directly porportional to its volume, and after 2 minutes, only 75 ml of the capsule's volume still remained. How long would it taje this capsule to lose half its volume.
With your help, i figured out the time needed for part 2.
> eq2 := diff(y(t), t) = -(1*k)*y(t);

> dsolve(eq2, y(t));

> k := .4836;

> dsolve({eq2, y(2) = 75.0}, y(t))

rhs(y(t) = 75*exp(-(1209/2500)*t)/exp(-1209/1250));

> fsolve(rhs(y(t) = 75*exp(-(1209/2500)*t)/exp(-1209/1250)) = 37.5, t);                                              =

3.433306825>

> From there two more questions are asked asking when will the two capsules start to dissolve at the same time and when will the difference in their volumes be the greatest and the rate of change of the volumes.

Ive tried jiggering poking around with the two equations: in part 1 and 2 and tried to use the fsolve command, but i had to deal with the dy/ dt which wont allow me to get an approximate answer.

All help is greatly appreciated and thank you! ﻿