The growth of a cell depends on the flow of nutrients through its surface. Let be the weight of the cell at time . Assume that for a limited time the growth rate is proportional to . (If the density remains constant, then is proportional to , where D is the diameter of the cell, and the surface area is proportional to , or equivalently ).

Hence for some positive constant . Find the general solution to this differential equation.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 4, p. 132)