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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 33

The temperature of water in a kettle is modelled using the equation T=75e−kt+25T = 75e^{-kt} + 25T=75e−kt+25

a.

Explain what the 25 represents in the equation T=75e−kt+25T = 75e^{-kt} + 25T=75e−kt+25

[1]
b.

When the kettle is turned off the rate of decrease of the water temperature is 20∘C20^{\circ}\text{C}20∘C per minute. Find the value of kkk

[3]
c.

Find how many minutes it takes for the water to cool to 55∘C55^{\circ}\text{C}55∘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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