4. A population of deer is introduced into a park. The population \(P\) at \(t\) years after the deer have been introduced is modelled by \(P = \frac { 2000 a ^ { t } } { 4 + a ^ { t } }\), where \(a\) is a constant. Given that there are 800 deer in the park after 6 years,

1. calculate, to 4 decimal places, the value of \(a\),
2. use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.
3. With reference to this model, give a reason why the population of deer cannot exceed 2000.