8 The rate of change of a certain population \(P\) at time \(t\) is modelled by the equation \(\frac { \mathrm { d } P } { \mathrm {~d} t } = ( 100 - P )\). Initially \(P = 2000\).
- Determine an expression for \(P\) in terms of \(t\).
- Describe how the population changes over time.