| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - direct proportionality (dN/dt = kN) |
| Difficulty | Moderate -0.3 This is a standard C4 exponential decay question with straightforward setup and solution. Part (a) requires forming and solving a separable differential equation (routine technique), while parts (b) and (c) involve substituting values and solving logarithmic equations. The question follows a predictable template with no novel insights required, making it slightly easier than average for A-level, though the multi-part structure and application context keep it close to typical difficulty. |
| Spec | 1.08l Interpret differential equation solutions: in context |
A Pancho car has value $£V$ at time $t$ years. A model for $V$ assumes that the rate of decrease of $V$ at time $t$ is proportional to $V$.
\begin{enumerate}[label=(\alph*)]
\item By forming and solving an appropriate differential equation, show that $V = Ae^{-kt}$, where $A$ and $k$ are positive constants. [3]
\end{enumerate}
The value of a new Pancho car is $£20\,000$, and when it is 3 years old its value is $£11\,000$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, to the nearest $£100$, an estimate for the value of the Pancho when it is 10 years old. [5]
\end{enumerate}
A Pancho car is regarded as 'scrap' when its value falls below $£500$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the approximate age of the Pancho when it becomes 'scrap'. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q23 [11]}}