7. A population \(P\) is growing at a rate which is modelled by the differential equation
$$\frac { d P } { d t } - 0.1 P = 0.05 t$$
where \(t\) years is the time that has elapsed from the start of observations.
It is given that the population is 10000 at the start of the observations.
- Solve the differential equation to obtain an expression for \(P\) in terms of \(t\).
- Show that the population doubles between the sixth and seventh year after the observations began.
(2)