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1.6.8 Reduction to linear form

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Question 37

The amount of a specific bacteria in a culture, $B$ , is modelled by the formula

B = pq^t

where $p$ and $q$ are constants and $t$ is the number of hours after the measurement began at 12:00 PM. A graph of $log_{10} B$ against $t$ is plotted based on data from the first 4 hours. The data points follow a straight line with a gradient of 0.12 and a vertical intercept on the $log_{10} B$ axis of 1.45.

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

[4]

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

[1]

Use the model to estimate the bacteria count at 8:00 PM on the same day.

[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 37

The amount of a specific bacteria in a culture, $B$ , is modelled by the formula

B = pq^t

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

[4]

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

[1]

Use the model to estimate the bacteria count at 8:00 PM on the same day.

[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.