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Exponentials and Logarithms

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Question 124

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=ke−0.15t+21,t≥0\theta = ke^{-0.15t} + 21, t \geq 0θ=ke−0.15t+21,t≥0, where k>19k>19k>19

a.

Sketch the graph of θ \theta\,θ against ttt.

[2]
b.

Find according to the model the initial temperature of the tea in terms of kkk.

[1]
c.

Find the value of t t\,t when the cup of tea reaches 40∘C40^\circ\text{C}40∘C, giving your answer in terms of kkk.

[3]
Markscheme

Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /Exponentials and Logarithms

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.

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