Mathematics 9709 · AS & A Level · Differential equations

Differential equations — practice question

A biologist is studying how a weed spreads across a particular region. At time $t$ weeks after the investigation begins, the area covered by the weed is $A \, \text{m}^2$. The biologist says that the rate at which $A$ increases is proportional to $\sqrt{(2A - 5)}$.
(i)[1]

Write down a differential equation that represents the biologist’s claim.

(ii)[9]

At the beginning of the investigation, the weed covered $7 \, \text{m}^2$, and $10$ weeks later, the covered area was $27 \, \text{m}^2$. If the biologist’s claim is assumed to be correct, find the area covered $20$ weeks after the start of the investigation.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $\frac{dA}{dt}=k\sqrt{2A-5}$ as the required equation.” …

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