We might also guess that the volume V of a melting snowball decreases at a rate proportional to its surface area. Argue as in Exercise 59 to find a differential equation satisfied by V. Suppose the snowball has volume 1000 cm³ and that it loses half of its volume after 5 minutes. According to this model, when will the snowball disappear?

Data From Exercise 59

According to one hypothesis, the growth rate dV/dt of a cell’s volume V is proportional to its surface area a. Since V has cubic units such as cm³ and A has square units such as cm², we may assume roughly that A ∝ V^2/3, and hence dV/dt = kV^2/3 for some constant k. If this hypothesis is correct, which dependence of volume on time would we expect to see (again, roughly speaking) in the laboratory?