| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential growth/decay model setup |
| Difficulty | Moderate -0.5 This is a straightforward exponential model question requiring substitution of given values to find constants, then using the model to predict a future value. The algebra is routine (substituting n=1 and n=2, dividing equations to eliminate A, then solving for b and A), and the final prediction is a simple calculation. Slightly easier than average due to the guided 'show that' part and minimal conceptual challenge. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b1.06i Exponential growth/decay: in modelling context |
3 The profit $\pounds P$ made by a company in its $n$th year is modelled by the exponential function
$$P = A \mathrm { e } ^ { b n }$$
In the first year (when $n = 1$ ), the profit was $\pounds 10000$. In the second year, the profit was $\pounds 16000$.\\
(i) Show that $\mathrm { e } ^ { b } = 1.6$, and find $b$ and $A$.\\
(ii) What does this model predict the profit to be in the 20th year?
\hfill \mbox{\textit{OCR MEI C3 2008 Q3 [8]}}