1.6 Exponentials and logarithms

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Question 9

A scientist is studying the relationship between the concentration of a chemical catalyst, $x\,$ units, and the time taken for a reaction to complete, $y\,$ seconds.

The scientist records data for 20 different concentrations and finds the product moment correlation coefficient between concentration and reaction time to be -0.35.

Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between concentration and reaction time.

[3]

The scientist proposes a power model and codes the data using $m = \log_{10}x$ and $n = \log_{10}y$ . The regression line is $n = 2.45 - 0.72 m$ .

The product moment correlation coefficient for the coded data is found to be -0.92.

Explain how this value supports the scientist's proposal.

[1]

Show that the relationship between $x\,$ and $y\,$ can be written in the form $y = ax^b$ where $a\,$ and $b\,$ are constants to be found.

[5]

1.6 Exponentials and logarithms

Question 9

A scientist is studying the relationship between the concentration of a chemical catalyst, $x\,$ units, and the time taken for a reaction to complete, $y\,$ seconds.

The scientist records data for 20 different concentrations and finds the product moment correlation coefficient between concentration and reaction time to be -0.35.

Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between concentration and reaction time.

[3]

The scientist proposes a power model and codes the data using $m = \log_{10}x$ and $n = \log_{10}y$ . The regression line is $n = 2.45 - 0.72 m$ .

The product moment correlation coefficient for the coded data is found to be -0.92.

Explain how this value supports the scientist's proposal.

[1]

Show that the relationship between $x\,$ and $y\,$ can be written in the form $y = ax^b$ where $a\,$ and $b\,$ are constants to be found.

[5]

1.6 Exponentials and logarithms

Question 9

Markscheme

1.6 Exponentials and logarithms

Question 9

Markscheme

1.6 Exponentials and logarithms

Question 9

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 9

1.6 Exponentials and logarithms Questions