| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Calculus with exponential models |
| Difficulty | Standard +0.8 Part (i) is a standard half-life calculation requiring straightforward logarithm manipulation. Part (ii) is more demanding: students must construct the second exponential model from given data, differentiate both functions, equate the rates of change, and solve—requiring multiple connected steps and understanding that 'rate of decay' means the derivative, which is less routine than typical A-level exponential questions. |
| Spec | 1.06i Exponential growth/decay: in modelling context1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
11 In a science experiment a substance is decaying exponentially. Its mass, $M$ grams, at time $t$ minutes is given by $M = 300 e ^ { - 0.05 t }$.\\
(i) Find the time taken for the mass to decrease to half of its original value.
A second substance is also decaying exponentially. Initially its mass was 400 grams and, after 10 minutes, its mass was 320 grams.\\
(ii) Find the time at which both substances are decaying at the same rate.
\hfill \mbox{\textit{OCR H240/01 2018 Q11 [11]}}