2026 CSS P2 Q3

An object is heated until it reaches a temperature of \(T\) degrees Celsius. It is then allowed to cool.

Its temperature \(T\) degrees Celsius when it is cooling for time \(t\) minutes is given by the equation \(T=28+72e^{-0.1t}\).

Find

1. the value of \(t\) (in minutes and seconds) when \(T=50\),[2]
2. the value of \(T\) when \(t=8\),[1]
3. the rate at which \(T\) is decreasing when \(t=4\),[2]
4. the highest temperature \(T_h\) and the approximate temperature \(T_A\) when \(t\) becomes very large.[2]