<p>A freshly brewed cup of tea, initially at a temperature of 85°C, is left out to cool in a room with a room temperature of 25°C. After 20 minutes, the temperature of the tea is 55°C.</p>
<p>It is known that the rate of change of the temperature of the tea is proportional to the difference between the temperature of the tea and the room temperature.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Given that&nbsp;\(\theta\) is the temperature of the tea \(t\) minutes after the tea is left out to cool, show that&nbsp;\(\theta = 25 + 60\mathrm{e}^{-kt}\), where&nbsp;\(k\) is a constant to be determined.<span class="inline-marks">[5]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Sketch the graph of \(\theta\) against \(t\).<span class="inline-marks">[2]</span></div></li></ol>

A freshly brewed cup of tea, initially at a temperature of 85°C, is left out to cool in a room with a room temperature of 25°C. After 20 minutes, the temperature of the tea is 55°C.

It is known that the rate of change of the temperature of the tea is proportional to the difference between the temperature of the tea and the room temperature.

Given that \(\theta\) is the temperature of the tea \(t\) minutes after the tea is left out to cool, show that \(\theta = 25 + 60\mathrm{e}^{-kt}\), where \(k\) is a constant to be determined.

Sketch the graph of \(\theta\) against \(t\).

2025 ACJC P1 Q7

2025 ACJC P1 Q7