| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential growth/decay model setup |
| Difficulty | Moderate -0.8 This is a straightforward exponential model question requiring basic substitution and logarithm manipulation. Part (i) is trivial (substitute t=0), and part (ii) involves one substitution followed by taking logarithms to solve for k—standard C2 material with no conceptual challenges or multi-step reasoning. |
| Spec | 1.06i Exponential growth/decay: in modelling context |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 11 000 | B1 | 1 mark |
| (ii) \(10^{3k} = \frac{24000}{11000} = 2.182 \Rightarrow 3k = \log 2.182 \Rightarrow k = 0.11\) | M1 M1 A1 | 3 marks |
**(i)** 11 000 | B1 | 1 mark
**(ii)** $10^{3k} = \frac{24000}{11000} = 2.182 \Rightarrow 3k = \log 2.182 \Rightarrow k = 0.11$ | M1 M1 A1 | 3 marks | Correct process for solution2 The growth in population $P$ of a certain town after time $t$ years can be modelled by the equation $P = 11000 \times 10 ^ { k t }$ where $k$ is a constant.\\
(i) State the initial population of the town.\\
(ii) After three years the population of the town is 24000 . Use this information to find the value of $k$ correct to two decimal places.
\hfill \mbox{\textit{OCR MEI C2 Q2 [4]}}