| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Finding x from given y value |
| Difficulty | Moderate -0.8 This is a straightforward exponential growth application requiring only direct substitution (t=3) and solving a simple exponential equation using logarithms. Both parts are standard textbook exercises with clear methods and minimal problem-solving demand, making it easier than average for A-level. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
During one day, a biological culture is allowed to grow under controlled conditions. At 8 a.m. the culture is estimated to contain 20000 bacteria. A model of the growth of the culture assumes that $t$ hours after 8 a.m., the number of bacteria present, $N$, is given by
$$N = 20000 \times (1.06)^t.$$
Using this model,
\begin{enumerate}[label=(\roman*)]
\item find the number of bacteria present at 11 a.m., [2]
\item find, to the nearest minute, the time when the initial number of bacteria will have doubled. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q3 [6]}}