| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Half-life and doubling time |
| Difficulty | Moderate -0.8 This is a straightforward application of exponential decay with standard half-life calculations. Part (i) involves simple substitution to find constants (A=100 is immediate, k found via ln(2)/1500), and part (ii) requires solving M=1 using the same exponential model. Both parts follow routine textbook procedures with no conceptual challenges or novel problem-solving required. |
| Spec | 1.06i Exponential growth/decay: in modelling context |
2 A radioactive substance decays exponentially, so that its mass $M$ grams can be modelled by the equation $M = A \mathrm { e } ^ { - k t }$, where $t$ is the time in years, and $A$ and $k$ are positive constants.\\
(i) An initial mass of 100 grams of the substance decays to 50 grams in 1500 years. Find $A$ and $k$.\\
(ii) The substance becomes safe when $99 \%$ of its initial mass has decayed. Find how long it will take before the substance becomes safe.
\hfill \mbox{\textit{OCR MEI C3 2009 Q2 [8]}}