| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Calculus with exponential models |
| Difficulty | Moderate -0.3 This is a straightforward exponential decay question requiring standard techniques: (i) solving an exponential equation using logarithms, and (ii) differentiating and solving for t when dm/dt equals a given value. Both parts are routine applications of C3 content with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.06i Exponential growth/decay: in modelling context1.07k Differentiate trig: sin(kx), cos(kx), tan(kx) |
A substance is decaying in such a way that its mass, $m$ kg, at a time $t$ years from now is given by the formula
$$m = 240e^{-0.04t}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the time taken for the substance to halve its mass. [3]
\item Find the value of $t$ for which the mass is decreasing at a rate of 2.1 kg per year. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [7]}}