9. 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,
- calculate, to 4 decimal places, the value of \(a\),
- use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.
- With reference to this model, give a reason why the population of deer cannot exceed 2000.
[0pt]
[P2 June 2001 Question 6]