The temperature of water in a kettle is modelled using the formula T=75e−kt+22T = 75e^{-kt} + 22T=75e−kt+22 Where T T\,T is the temperature t t\,t minutes after the kettle is turned off and k k\,k is a positive constant.
Find the rate of change of the temperature in terms of kkk
After 5 minutes the temperature of the water is 70∘C70^{\circ}\text{C}70∘C. Find the value of kkk
Find how many minutes it takes for the water to cool to 55∘C55^{\circ}\text{C}55∘C
Practise AQA A Level Maths 1.9 F: Exponentials and logarithms with exam-style questions for A Level Maths. 37 questions covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 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.
