| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| 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 modelling question requiring substitution of given conditions and basic algebraic manipulation. Part (i) uses limiting behaviour (as tââ, e^{-kt}â0) and initial conditions (t=0), which are standard techniques. Part (ii) involves solving a logarithmic equation. All steps are routine for C3 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
The height $h$ metres of a tree after $t$ years is modelled by the equation
$$h = a - be^{-kt},$$
where $a$, $b$ and $k$ are positive constants.
\begin{enumerate}[label=(\roman*)]
\item Given that the long-term height of the tree is 10.5 metres, and the initial height is 0.5 metres, find the values of $a$ and $b$. [3]
\item Given also that the tree grows to a height of 6 metres in 8 years, find the value of $k$, giving your answer correct to 2 decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q4 [6]}}