| 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 | Standard +0.3 This is a straightforward C2 logarithms question requiring substitution to find a constant, then solving an equation involving logs, and interpreting a limit. All steps are routine applications of standard techniques with clear signposting, making it slightly easier than average. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
A population of deer is introduced into a park. The population P at t years after the deer have been introduced is modelled by
$$P = \frac{2000a^t}{4 + a^t},$$
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, [4]
\item use the model to predict the number of years needed for the population of deer to increase from 800 to 1800. [4]
\item With reference to this model, give a reason why the population of deer cannot exceed 2000. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [9]}}