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1.6.8 Reduction to linear form

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Question 17

The light intensity, $I$ lux, measured after passing through $n$ layers of a specific optical filter, is modelled by the relationship $I = ab^n$ where $a$ and $b$ are constants. Experimental data for the first 5 layers is used to plot a graph of $log_{10} I$ against $n$ . The data points are found to lie on a straight line with a gradient of $- 0.11$ and a vertical intercept of $2.45$ on the $log_{10} I$ axis.

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

[4]

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

[1]

Use the model to estimate the light intensity when 8 layers of the filter are used.

[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 17

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

[4]

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

[1]

Use the model to estimate the light intensity when 8 layers of the filter are used.

[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.