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1.6.8 Reduction to linear form

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Question 22

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]

1.6.8 Reduction to linear form Questions

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