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1.6.8 Reduction to linear form

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Question 13

The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

[3]

Give an interpretation of the constant $a\,$ in this equation.

[1]

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]

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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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Question 13

The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

[3]

Give an interpretation of the constant $a\,$ in this equation.

[1]

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]

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.