- A population of deer was introduced onto an island.
The number of deer, \(P\), on the island at time \(t\) years following their introduction is modelled by the differential equation
$$\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { P } { 5000 } \left( 1000 - \frac { P ( t + 1 ) } { 6 t + 5 } \right) \quad t > 0$$
It was estimated that there were 540 deer on the island six months after they were introduced.
Use two applications of the approximation formula \(\left( \frac { \mathrm { d } y } { \mathrm {~d} x } \right) _ { n } \approx \frac { y _ { n + 1 } - y _ { n } } { h }\) to estimate the number of deer on the island 10 months after they were introduced.