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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 25

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

a.

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

[2]
b.

Find according to the model the initial temperature of the tea.

[1]
c.

Find the value of t t\,t when the cup of tea reaches 40∘C40^\circ\text{C}40∘C.

[3]
Markscheme

1.6 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.6 Exponentials and Logarithms

104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.

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