- The number of people, \(n\), in a queue at a Post Office \(t\) minutes after it opens is modelled by the differential equation
$$\frac { \mathrm { d } n } { \mathrm {~d} t } = \mathrm { e } ^ { 0.5 t } - 5 , \quad t \geq 0$$
- Find, to the nearest second, the time when the model predicts that there will be the least number of people in the queue.
- Given that there are 20 people in the queue when the Post Office opens, solve the differential equation.
- Explain why this model would not be appropriate for large values of \(t\).