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1.6 Exponentials and Logarithms

1.6 Exponentials and Logarithms

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Question 46

The signal intensity, SSS (measured in nanowatts), of a specialized acoustic transducer is monitored during a calibration phase. The intensity is modelled by the equation

log⁡10S=0.64+0.035h \log_{10} S = 0.64 + 0.035h log10​S=0.64+0.035h

where h h\,h is the time in minutes after calibration began.

Use the equation of the model to answer parts (a) and (b).

a.

Find the initial signal intensity of the transducer, giving your answer to 2 decimal places.

[2]
b.

After T T\,T minutes, the signal intensity reaches 480 nanowatts. Find the value of TTT, giving your answer to 2 decimal places.

[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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