| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 21 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Time to reach target in exponential model |
| Difficulty | Moderate -0.8 This question requires only direct substitution into a given formula. Part (i) involves calculating years elapsed (2012 minus some base year, likely 1900 or similar from context), and part (ii) requires evaluating the exponential expression with that t-value. Both are straightforward calculator exercises with no conceptual challenge or problem-solving required. |
| Spec | 1.06i Exponential growth/decay: in modelling context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(t = 2012 - 1900 = 112\) (or equivalent depending on base year used in model) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Substituting their \(t\) into \(R = 115 + 60e^{-0.0467t^{0.797}}\) | M1 | |
| \(R \approx 120.8\) minutes (or equivalent in minutes and seconds \(\approx\) 2 hours 0 minutes 48 seconds) | A1 | cao |
# Question 6(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $t = 2012 - 1900 = 112$ (or equivalent depending on base year used in model) | B1 | |
# Question 6(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Substituting their $t$ into $R = 115 + 60e^{-0.0467t^{0.797}}$ | M1 | |
| $R \approx 120.8$ minutes (or equivalent in minutes and seconds $\approx$ 2 hours 0 minutes 48 seconds) | A1 | cao |6 A number of cases of the general exponential model for the marathon are given in Table 6. One of these is
$$R = 115 + ( 175 - 115 ) \mathrm { e } ^ { - 0.0467 t ^ { 0.797 } }$$
(i) What is the value of $t$ for the year 2012?\\
(ii) What record time does this model predict for the year 2012?\\
(i) $\_\_\_\_$\\
(ii) $\_\_\_\_$\\
\hfill \mbox{\textit{OCR MEI C4 2006 Q6 [21]}}