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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 64

A telecommunications engineer is investigating the signal intensity, SSS (measured in picowatts), at a distance ddd (measured in metres) from a radio transmitter. The relationship is modelled by S=adbS = ad^bS=adb, where a a\,a and b b\,b are constants.

A graph shows a linear relationship between log⁡10S\log_{10} Slog10​S and log⁡10d\log_{10} dlog10​d. The line passes through the points (1,8)(1, 8)(1,8) and (4,2)(4, 2)(4,2).

a.

Find an equation linking log⁡10S\log_{10} Slog10​S with log⁡10d\log_{10} dlog10​d.

[3]
b.

Hence, or otherwise, express S S\,S in the form adbad^badb, where a a\,a and b b\,b are constants to be found.

[2]
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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