| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Logistic growth model |
| Difficulty | Standard +0.3 This is a structured multi-part question on exponential modeling that requires algebraic manipulation and understanding of asymptotic behavior. Part (a) involves substituting and solving for a constant (routine but requires careful algebra), part (b) requires setting up and solving two equations to find a time difference (standard technique), and part (c) tests conceptual understanding of limits. While it has multiple steps and 9 marks total, each part follows predictable C2-level techniques without requiring novel insight or particularly challenging problem-solving. |
| 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 Q9 [9]}}