| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential model with shifted asymptote |
| Difficulty | Standard +0.3 This is a straightforward application of exponential functions requiring substitution (part a), solving an exponential equation (part b), and differentiation followed by evaluation (part c). All techniques are standard C3 material with no novel insight required, though the shifted asymptote and two exponential terms add minor complexity beyond the most basic examples. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context1.07j Differentiate exponentials: e^(kx) and a^(kx) |
\begin{enumerate}
\item The value of Bob's car can be calculated from the formula
\end{enumerate}
$$V = 17000 \mathrm { e } ^ { - 0.25 t } + 2000 \mathrm { e } ^ { - 0.5 t } + 500$$
where $V$ is the value of the car in pounds $( \pounds )$ and $t$ is the age in years.\\
(a) Find the value of the car when $t = 0$\\
(b) Calculate the exact value of $t$ when $V = 9500$\\
(c) Find the rate at which the value of the car is decreasing at the instant when $t = 8$. Give your answer in pounds per year to the nearest pound.
\hfill \mbox{\textit{Edexcel C3 2013 Q8 [9]}}