STATEMENT OF PROBLEM

Part A - A spherical capsule has volume V and surface area S. Assume that this capsule dissolves in a certain solution such that the rate of change in volume, dV/dt, is directly proportional to the capsule's surface area.


Show that dV/dt = - k (V^(2/3)) for some k > 0.

Part B - Assuming k = .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?

Part C - Assuming the same size capsule as in part B, what if the change in volume of this second capsule were instead directly proportional to its volume, and after 2 minutes, only 75 ml of the capsule volume still remained.


This might occur if the capsule is permeated by liquid and the small granuals contained in the capsule are each dissolving on their own. How long would it take this capsule to lose half its volume?

Part D - If the two capsules in part B and C start to dissolve at the same time, when will the difference in their volumes be the greatest?

Part E - For the two capsules in part B and C, when is the rate of change of the volumes of both capsules the same?