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.
7 exam-style questions on Edexcel A Level Old Maths Logs. Each one has a worked solution and a mark scheme showing where the marks go.