<ol class="abc-list"><li><div class="list-item-paragraph">An insect population in $2023$ is $3.7$ million.<br>The insect population has been decreasing at a rate of $12\%$ per year.<br>What was the insect population in $2015$?<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Sue invests $\$x$ in County Bank for&nbsp;$3$ years.<br>Amy invests $\$x$ in Best Investments for&nbsp;$3$ years.</div><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 250px;"><col style="width: 250px;"></colgroup><tbody><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>County Bank</strong></p><p>Compound Interest</p><p>${2\%}$ per year for the first two years</p><p>${3.5\%}$ per year for each extra year</p></td><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>Best Investments</strong></p><p>Compound Interest</p><p>${r\%}$ per year</p></td></tr><tr></tr></tbody></table></div><div class="list-item-paragraph">At the end of ${3}$ years, they each receives ${\$34\;458.05}$</div><ol class="i-list"><li><div class="list-item-paragraph">Show that Sue's initial investment is $\$32\ 000$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the value of $r$.<span class="inline-marks">[2]</span></div></li></ol></li></ol>

An insect population in $2023$ is $3.7$ million.
The insect population has been decreasing at a rate of $12\%$ per year.
What was the insect population in $2015$?

Sue invests $\$x$ in County Bank for $3$ years.
Amy invests $\$x$ in Best Investments for $3$ years.

At the end of ${3}$ years, they each receives ${\$34\;458.05}$