| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | First-order integration |
| Difficulty | Moderate -0.3 This is a straightforward C4 differential equations question requiring basic integration and interpretation. Part (i) involves setting the derivative to zero (simple exponential equation), part (ii) is direct integration with an initial condition, and part (iii) asks for a contextual comment. All techniques are standard with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
6. The number of people, $n$, in a queue at a Post Office $t$ minutes after it opens is modelled by the differential equation
$$\frac { \mathrm { d } n } { \mathrm {~d} t } = \mathrm { e } ^ { 0.5 t } - 5 , \quad t \geq 0$$
(i) Find, to the nearest second, the time when the model predicts that there will be the least number of people in the queue.\\
(ii) Given that there are 20 people in the queue when the Post Office opens, solve the differential equation.\\
(iii) Explain why this model would not be appropriate for large values of $t$.\\
\hfill \mbox{\textit{OCR C4 Q6 [8]}}