<p>A metal container of hot liquid is left to cool in a laboratory. The temperature of the liquid, $T$ °C, after $n$ minutes is given by $T = a\mathrm{e}^{-kn} + 15$, where&nbsp;$a$ and $k$ are constants. The table below shows the measured values of $T$ and $n$.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 475px;"><colgroup><col style="width: 100px;"><col style="width: 75px;"><col style="width: 75px;"><col style="width: 75px;"><col style="width: 75px;"><col style="width: 75px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$n$ (minutes)</th><th style="text-align: center; --cell-justify: center"><p>$10$<br></p></th><th style="text-align: center; --cell-justify: center"><p>$20$<br></p></th><th style="text-align: center; --cell-justify: center"><p>$30$<br></p></th><th style="text-align: center; --cell-justify: center"><p>$40$<br></p></th><th style="text-align: center; --cell-justify: center"><p>$50$<br></p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$T$ °C</td><td style="text-align: center; --cell-justify: center"><p>$66.9$<br></p></td><td style="text-align: center; --cell-justify: center"><p>$46.5$<br></p></td><td style="text-align: center; --cell-justify: center"><p>$35.1$<br></p></td><td style="text-align: center; --cell-justify: center"><p>$27.2$<br></p></td><td style="text-align: center; --cell-justify: center"><p>$22.4$<br></p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-1"><div class="list-item-paragraph">Plot $\ln(T - 15)$ against $n$ and draw a straight line graph to illustrate the information.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-2"><div class="list-item-paragraph">Use your graph to estimate</div><ol class="i-list"><li data-list-item-id="subitem-1781513691409-p74c35pzo"><div class="list-item-paragraph">the value of $k$<span class="inline-marks">[2]</span></div></li><li data-list-item-id="subitem-1781513691756-y3opx9sk6"><div class="list-item-paragraph">the number of minutes it takes for the temperature of the liquid to drop to $40 \%$ of its initial value.<span class="inline-marks">[3]</span></div></li></ol></li></ol>
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A metal container of hot liquid is left to cool in a laboratory. The temperature of the liquid, $T$ °C, after $n$ minutes is given by $T = a\mathrm{e}^{-kn} + 15$, where $a$ and $k$ are constants. The table below shows the measured values of $T$ and $n$.

Plot $\ln(T - 15)$ against $n$ and draw a straight line graph to illustrate the information.

2024 GESS PRELIMS P1 Q14

2024 GESS PRELIMS P1 Q14