| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential growth/decay model setup |
| Difficulty | Moderate -0.8 This is a straightforward exponential model question requiring only direct substitution to find constants and then solving a simple exponential equation using logarithms. All steps are routine C4 techniques with no problem-solving insight needed—easier than average A-level questions. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06d Natural logarithm: ln(x) function and properties1.06g Equations with exponentials: solve a^x = b |
2 The average weekly pay of a footballer at a certain club was $\pounds 80$ on 1 August 1960. By 1 August 1985, this had risen to $\pounds 2000$.
The average weekly pay of a footballer at this club can be modelled by the equation
$$P = A k ^ { t }$$
where $\pounds P$ is the average weekly pay $t$ years after 1 August 1960, and $A$ and $k$ are constants.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Write down the value of $A$.
\item Show that the value of $k$ is 1.137411 , correct to six decimal places.
\end{enumerate}\item Use this model to predict the year in which, on 1 August, the average weekly pay of a footballer at this club will first exceed $\pounds 100000$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2011 Q2 [6]}}