A heated metal ball is dropped into a liquid. As the ball cools, its temperature, TTT °C, t t\,t minutes after it enters the liquid, is given by
T=400e−0.05t+25,t≥0. T = 400e^{-0.05t} + 25, \quad t \geq 0. T=400e−0.05t+25,t≥0.Find the temperature of the ball as it enters the liquid.
Find the value of t t\,t for which T=300T = 300T=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=50t = 50t=50. Give your answer in °C per minute to 3 significant figures.
From the equation for temperature T T\,T in terms of ttt, given above, explain why the temperature of the ball can never fall to 20 °C.
Practise Edexcel A Level Old Maths Logs with exam-style questions for A Level Old Maths. 16 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.