The rate, in cm³ s⁻¹, at which oil is leaking from an engine sump at any time t seconds is proportional to the volume of oil, V cm3, in the sump at that instant. At time t = 0, V = A.

a. By forming and integrating a differential equation, show that V = Ae^−kt. where k is a positive constant.

b. Sketch a graph to show the relation between V and t. Given further that V = 1/2 A at t = T,

c. Show that kT = ln 2.