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1.6.8 Reduction to linear form

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Question 22

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

A = ab^t

where $a$ and $b$ are constants and $t$ is the number of days after the fire was first detected at 6:00 AM on Monday. A graph of $log_{10} A$ against $t$ 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 $log_{10} A$ axis of 0.85.

Determine the value of $a$ and the value of $b$ according to the model, rounding your answers to two decimal places.

[3]

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

[1]

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

[2]

Markscheme

1.6.8 Reduction to linear form Questions

A Level
Maths
1.6.8 Reduction to linear form

42 exam-style questions on OCR A Level Maths 1.6.8 Reduction to linear form. Each one has a worked solution and a mark scheme showing where the marks go.

1.6.8 Reduction to linear form

Question bank

1.6.8 Reduction to linear form

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Question 22

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

A = ab^t

Determine the value of $a$ and the value of $b$ according to the model, rounding your answers to two decimal places.

[3]

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

[1]

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

[2]

Markscheme

1.6.8 Reduction to linear form Questions

A Level
Maths
1.6.8 Reduction to linear form

42 exam-style questions on OCR A Level Maths 1.6.8 Reduction to linear form. Each one has a worked solution and a mark scheme showing where the marks go.