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.
Practise Edexcel A Level Maths Exponentials and Logarithms with exam-style questions for A Level Maths. 41 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.
