2026 RI P1 Q7

Conservationists are investigating the effect of habitat loss on the number of deer on an island. They observe that the population of the deer on the island decreases at a rate of \(2\%\) every year. The number of deer on the island is \(P\) at a time \(t\) years after conservationists begin observations.

1. Write down a differential equation relating \(P\) and \(t\).[1]

To maintain population stability, the conservationists relocate deer to the island at a constant uniform rate of \(h\) deer per year.

2. Write down a differential equation to model the new situation.[1]
3. Without solving the differential equation, determine the value of \(h\) if the conservationists would like the number of deer to settle down to \(600\) after many years.[2]
4. Solve the differential equation to find an expression for \(P\) in terms of \(t\) and \(h\). Hence, state the population of the deer, in terms of \(h\), in the long term.[5]