CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1 · Question Q40

Water is leaking from a tank. The rate of change in volume of water in the tank with respect to time, t, is inversely proportional to the volume, V, of water in the tank. If k is a positive constant of proportionality, then the equation that models this situation is

1. (A)\frac{dV}{dt} = \frac{-k}{V}
2. (B)V = \frac{-k}{\sqrt{t}}
3. (C)\frac{dV}{dt} = k\sqrt[3]{V}
4. (D)V = -kt