- Julie decides to start a business breeding rabbits to sell as pets.
Initially she buys 20 rabbits. After \(t\) years the number of rabbits, \(R\), is modelled by the differential equation
$$\frac { \mathrm { d } R } { \mathrm {~d} t } = 2 R + 4 \sin t \quad t > 0$$
Julie needs to have at least 40 rabbits before she can start to sell them.
Use two iterations of the approximation formula
$$\left( \frac { \mathrm { d } y } { \mathrm {~d} x } \right) _ { n } \approx \frac { y _ { n + 1 } - y _ { n } } { h }$$
to find out if, according to the model, Julie will be able to start selling rabbits after 4 months.