2026 CCHY P1 Q4

In a laboratory, the temperature, \(T\,{}^\circ\mathrm C\), of a chemical solution is being monitored \(t\) seconds after the cooling process has started. The rate of change of the temperature is given by \(\dfrac{\mathrm{d}T}{\mathrm{d}t}=-4e^{-0.04t}\). The initial temperature of the solution is \(90^\circ\mathrm C\).

1. Find an expression for \(T\), in terms of \(t\).[3]
2. A chemical indicator is to be added when the temperature reaches \(40^\circ\mathrm C\). How many seconds after the cooling process has started should the indicator be added?[2]
3. Will the temperature of the solution reach \(-15^\circ\mathrm C\)? Explain your answer clearly.[1]