Part E

Since the first derivative gives us the rate of change of the volumes we seek when these two functions are equal.

Input := 


p3=Plot[{v'[t],v2'[t]},{t,0,endTime}]

When the difference of the two functions is zero, the two functions have the same value.

There are two values of t for which the first derivatives are equal but only one in the realistic domain before one of the capsule models predicts the capsule is all gone. And hence it is at this one time, t = 1.57 min, that the capsules are shrinking at the same rate.