- Rabbits were introduced onto an island. The number of rabbits, \(P , t\) years after they were introduced is modelled by the equation
$$P = 80 \mathrm { e } ^ { \frac { 1 } { 5 } t } , \quad t \in \mathbb { R } , t \geqslant 0$$
- Write down the number of rabbits that were introduced to the island.
- Find the number of years it would take for the number of rabbits to first exceed 1000.
- Find \(\frac { \mathrm { d } P } { \mathrm {~d} t }\).
- Find \(P\) when \(\frac { \mathrm { d } P } { \mathrm {~d} t } = 50\).