CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1 · Question Q43

Water is leaking from a tank. The rate of change in volume of the 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)V = \frac{-k}{\sqrt{t}}
2. (B)\frac{dV}{dt} = \frac{-k}{V}
3. (C)\frac{dV}{dt} = -k\sqrt{V}
4. (D)V = -kt