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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 45

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

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.

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