| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| 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 (routine algebraic manipulation), and (ii) differentiating an exponential function and substituting a value. Both parts are direct applications of C3 content with no problem-solving insight required, making it slightly easier than average but not trivial since it involves multiple steps and careful handling of the exponential function. |
| Spec | 1.06g Equations with exponentials: solve a^x = b1.06i Exponential growth/decay: in modelling context1.07j Differentiate exponentials: e^(kx) and a^(kx) |
The mass, $m$ grams, of a substance at time $t$ years is given by the formula
$$m = 180e^{-0.017t}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the value of $t$ for which the mass is 25 grams. [3]
\item Find the rate at which the mass is decreasing when $t = 55$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q3 [6]}}