The temperature, θ∘C\theta^\circ\text{C}θ∘C, of a cup of tea t t\,t minutes after measurements began, is modelled using the formula θ=68e−0.15t+21,t≥0\theta = 68e^{-0.15t} + 21, t \geq 0θ=68e−0.15t+21,t≥0
Sketch the graph of θ \theta\,θ against ttt.
Find according to the model the initial temperature of the tea.
Find the value of t t\,t when the cup of tea reaches 40∘C40^\circ\text{C}40∘C.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, 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. Each one has a worked solution and a mark scheme showing where the marks go.