| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Logistic growth model |
| Difficulty | Challenging +1.2 This logistic growth question requires algebraic manipulation to find the constant (substitution and solving an exponential equation), then solving another exponential equation for time, and finally interpreting the model's limiting behavior. While it involves multiple steps and understanding of asymptotic behavior, the techniques are relatively standard for C2 level—substitution, logarithms, and limit analysis—making it moderately above average difficulty but not requiring deep insight. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
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,
\begin{enumerate}[label=(\alph*)]
\item calculate, to 4 decimal places, the value of $a$,
\item use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.
\item With reference to this model, give a reason why the population of deer cannot exceed 2000.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [9]}}