Mathematics 9709 · AS & A Level · Differential equations

Differential equations — practice question

Naturalists are running a wildlife reserve to raise the population of a rare plant species. The number of plants after $t$ years is represented by $N$, with $N$ taken as a continuous variable.
(a(i))[1]

You are told that the rate of increase of $N$ with respect to $t$ is proportional to $(N - 150)$. Write a differential equation involving $N$, $t$ and a constant of proportionality.

(a(ii))[7]

At the start, when $t = 0$, there were $650$ plants. It was observed that, at a point when the count had reached $900$, the plants were increasing at $60$ per year. Write $N$ as a function of $t$.

(a(iii))[2]

The naturalists wanted the number of plants to rise from $650$ to $2000$ in $15$ years. Is this target achieved?

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: State the equation $\dfrac{dN}{dt}=k(N-150)$

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