2025 BVSS PRELIMS P2 Q2

Hot coffee is heated to a temperature of \(90^\circ\text{C}\). The temperature, \(T^\circ\text{C}\), \(t\) minutes after removal from the heat source is given by \(T=22+Ae^{kt}\), where \(A\) and \(k\) are constants.

1. Explain why \(A=68\).[1]
2. After 3.5 minutes, the temperature of coffee is \(79^\circ\text{C}\). Find \(k\).[3]
3. The coffee should only be served when it is between \(55^\circ\text{C}\) to \(70^\circ\text{C}\). Determine, with working, whether the coffee is suitable to be served 10 minutes after removal from the heat source.[2]
4. After a long time, \(T\) approaches a value. Calculate this value.[1]