| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Exponential Functions |
| Type | Rate of change in exponential model |
| Difficulty | Moderate -0.8 This is a straightforward exponential growth question requiring basic understanding of the model (parts a,b), a routine logarithm calculation (part c), and qualitative reasoning about model limitations (part d). All techniques are standard AS-level with no novel problem-solving required, making it easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context1.07b Gradient as rate of change: dy/dx notation |
The number of members of a social networking site is modelled by $m = 150e^{2t}$, where $m$ is the number of members and $t$ is time in weeks after the launch of the site.
\begin{enumerate}[label=(\alph*)]
\item State what this model implies about the relationship between $m$ and the rate of change of $m$. [2]
\item What is the significance of the integer 150 in the model? [1]
\item Find the week in which the model predicts that the number of members first exceeds 60 000. [3]
\item The social networking site only expects to attract 60 000 members.
Suggest how the model could be refined to take account of this. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q3 [7]}}