| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Finding x from given y value |
| Difficulty | Moderate -0.3 This is a straightforward exponential decay application requiring only direct substitution, basic logarithm manipulation, and solving simultaneous equations. All techniques are standard C3 material with no conceptual challenges—slightly easier than average due to the guided structure and routine calculations. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
The value $£V$ of a car $t$ years after it is new is modelled by the equation $V = Ae^{-kt}$, where $A$ and $k$ are positive constants which depend on the make and model of the car.
\begin{enumerate}[label=(\roman*)]
\item Brian buys a new sports car. Its value is modelled by the equation
$$V = 20000 e^{-0.2t}.$$
Calculate how much value, to the nearest £100, this car has lost after 1 year. [2]
\item At the same time as Brian buys his car, Kate buys a new hatchback for £15000. Her car loses £2000 of its value in the first year. Show that, for Kate's car, $k = 0.143$ correct to 3 significant figures. [3]
\item Find how long it is before Brian's and Kate's cars have the same value. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2014 Q6 [8]}}