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1.6 Exponentials and logarithms

1.6 Exponentials and logarithms

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Question 52

The total area, AAA hectares, affected by a wildfire is modelled by the formula

A=abt A = ab^t A=abt

where aaa and bbb are constants and ttt is the number of days after the fire was first detected at 6:00 AM on Monday. A graph of log⁡10A\log_{10} Alog10​A against ttt is plotted for the first 3 days. The data points form a straight line with a gradient of 0.14 and a vertical intercept on the log⁡10A\log_{10} Alog10​A axis of 0.85.

a.

Determine the value of aaa and the value of bbb according to the model, rounding your answers to two decimal places.

[3]
b.

Provide a practical interpretation of the constant aaa in the context of this model.

[1]
c.

Use the model to estimate the area affected by the wildfire at 6:00 AM on the following Saturday.

[2]
Markscheme

1.6 Exponentials and logarithms Questions

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

104 exam-style questions on WJEC A Level Maths 1.6 Exponentials and logarithms, covering 1.6.1 Exponentials and logarithms, 1.6.2 Exponentials and logarithms, 1.6.3 Exponentials and logarithms, 1.6.4 Exponentials and logarithms, 1.6.5 Exponentials and logarithms, 1.6.6 Exponentials and logarithms, 1.6.7 Exponentials and logarithms, 1.6.8 Exponentials and logarithms, and 1.6.9 Exponentials and logarithms. Each one has a worked solution and a mark scheme showing where the marks go.

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