| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential model with shifted asymptote |
| Difficulty | Moderate -0.3 This is a standard exponential decay modeling question with shifted asymptote. Students substitute given conditions to find constants (straightforward algebra), then solve for time using logarithms. All steps are routine C3 techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.06i Exponential growth/decay: in modelling context |
2 The temperature $T$ in degrees Celsius of water in a glass $t$ minutes after boiling is modelled by the equation $T = 20 + b \mathrm { e } ^ { - k t }$, where $b$ and $k$ are constants. Initially the temperature is $100 ^ { \circ } \mathrm { C }$, and after 5 minutes the temperature is $60 ^ { \circ } \mathrm { C }$.\\
(i) Find $b$ and $k$.\\
(ii) Find at what time the temperature reaches $50 ^ { \circ } \mathrm { C }$.
\hfill \mbox{\textit{OCR MEI C3 2010 Q2 [6]}}