2025 SST PRELIMS P2 Q3

A metal cube is heated to a temperature of \(205^\circ\mathrm{C}\) before being dropped into a liquid. As the cube cools, its temperature, \(T^\circ\mathrm{C}\), \(t\) minutes after it enters the liquid is given by \(T = K + 175e^{-mt}\), where \(K\) and \(m\) are constants.

2. Show that the value of \(K\) is 30.[1]
3. When \(t = 3\), the temperature of the cube reaches \(128^\circ\mathrm{C}\). Find the value of \(m\).[3]
4. Find the rate at which the temperature of the cube is decreasing at the instant when \(t = 8\).[3]
5. Explain why the temperature of the cube can never fall below \(30^\circ\mathrm{C}\).[2]