- A heated metal ball is dropped into a liquid. As the ball cools, its temperature, \(T ^ { \circ } \mathrm { C }\), \(t\) minutes after it enters the liquid, is given by
$$T = 400 \mathrm { e } ^ { - 0.05 t } + 25 , \quad t \geqslant 0$$
- Find the temperature of the ball as it enters the liquid.
- Find the value of \(t\) for which \(T = 300\), giving your answer to 3 significant figures.
- Find the rate at which the temperature of the ball is decreasing at the instant when \(t = 50\). Give your answer in \({ } ^ { \circ } \mathrm { C }\) per minute to 3 significant figures.
- From the equation for temperature \(T\) in terms of \(t\), given above, explain why the temperature of the ball can never fall to \(20 ^ { \circ } \mathrm { C }\).