<p>Two scientists are investigating the change of a certain population of size $n$ thousand at time $t$ years.</p>
<ol class="i-list"><li><div class="list-item-paragraph">One scientist suggests that $n$ and $t$ are related by the differential equation $\frac{{{\mathrm{d}}^{2}}n}{\mathrm{d}{{t}^{2}}}=10-6t$. Find the general solution of this differential equation. Sketch three members of the family of solution curves, given that $n=100$ when $t=0$.<span class="inline-marks">[5]</span></div></li><li><div class="list-item-paragraph">The other scientist suggests that $n$ and $t$ are related by the differential equation $\frac{\mathrm{d}n}{\mathrm{d}t}=3-0.02n$. Find $n$ in terms of $t$, given again that $n=100$ when $t=0$. Explain in simple terms what will eventually happen to the population using this model.<span class="inline-marks">[7]</span></div></li></ol>

Two scientists are investigating the change of a certain population of size $n$ thousand at time $t$ years.

One scientist suggests that $n$ and $t$ are related by the differential equation $\frac{{{\mathrm{d}}^{2}}n}{\mathrm{d}{{t}^{2}}}=10-6t$. Find the general solution of this differential equation. Sketch three members of the family of solution curves, given that $n=100$ when $t=0$.

The other scientist suggests that $n$ and $t$ are related by the differential equation $\frac{\mathrm{d}n}{\mathrm{d}t}=3-0.02n$. Find $n$ in terms of $t$, given again that $n=100$ when $t=0$. Explain in simple terms what will eventually happen to the population using this model.

N2009 P2 Q4

N2009 P2 Q4

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