| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2020 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - approach to limit (dN/dt = k(N - Nâ‚€)) |
| Difficulty | Standard +0.3 This is a straightforward separable differential equation with standard integration techniques. Part (a) requires separation of variables, partial fractions (or recognizing ln|100-P|), and applying initial conditions—all routine A-level methods. Part (b) is a simple interpretation of the solution. The question is slightly easier than average because it follows a standard template with no conceptual surprises, though the negative growth (P starts above equilibrium) adds minor interest. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
The rate of change of a certain population $P$ at time $t$ is modelled by the equation $\frac{dP}{dt} = (100 - P)$.
Initially $P = 2000$.
\begin{enumerate}[label=(\alph*)]
\item Determine an expression for $P$ in terms of $t$. [7]
\item Describe how the population changes over time. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2020 Q8 [9]}}