The diagram shows the curve \(\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }\).
\includegraphics[max width=\textwidth, alt={}, center]{a0d9573f-8273-4562-a2d3-07f15d9da1af-5_574_682_315_328}
On the axes in the Printed Answer Booklet, sketch graphs of
\(\frac { \mathrm { dy } } { \mathrm { dx } }\) against \(x\),
\(\frac { \mathrm { dy } } { \mathrm { dx } }\) against \(y\).
Wolves were introduced to Yellowstone National Park in 1995.
The population of wolves, \(y\), is modelled by the equation
\(y = A e ^ { k t }\),
where \(A\) and \(k\) are constants and \(t\) is the number of years after 1995.
Give a reason why this model might be suitable for the population of wolves.
When \(t = 0 , y = 21\) and when \(t = 1 , y = 51\).
Find values of \(A\) and \(k\) consistent with the data.
Give a reason why the model will not be a good predictor of wolf populations many years after 1995.