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=48e−0.1t+18,t≥0\theta = 48e^{-0.1t} + 18, t \geq 0θ=48e−0.1t+18,t≥0
Sketch the graph of θ \theta\,θ against ttt.
Find according to the model the initial temperature of the tea.
Show that when the cup of tea reaches 42∘C42^\circ\text{C}42∘C, e−0.1t=12\displaystyle e^{-0.1t}=\frac12e−0.1t=21.
Hence find the value of t t\,t when the cup of tea reaches 42∘C42^\circ\text{C}42∘C.
277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.