Mothballs tend to evaporate at a rate proportional to their surface area. If V is the volume of a mothball, then its surface area is roughly a constant times V^2/3. So the mothball’s volume decreases at a rate proportional to V^2/3. Suppose that initially a mothball has a volume of 27 cubic centimeters and 4 weeks later has a volume of 15.625 cubic centimeters. Construct and solve a differential equation satisfied by the volume at time t. Then, determine if and when the mothball will vanish (V = 0).