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2.2.2 Scatter diagrams and correlation

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Question 5

The number of bacteria, $N$ , in a colony is recorded $t\,$ hours after an experiment begins.

The data are coded using the changes of variable $x = t$ and $y = \log_{10} N$ .

The regression line of $y\,$ on $x\,$ is found to be

$y = 2.10 + 0.18 x$

Given that the data can be modelled by an equation of the form $N = ab^{t}$ , where $a\,$ and $b\,$ are constants, find the value of $a\,$ and the value of $b$ . Give your answers to 3 significant figures.

[3]

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

[1]

Explain why this model is unlikely to be reliable for predicting the number of bacteria one week after the experiment begins.

[1]

Markscheme

2.2.2 Scatter diagrams and correlation Questions

A Level
Maths
2.2.2 Scatter diagrams and correlation

157 exam-style questions on AQA A Level Maths 2.2.2 Scatter diagrams and correlation. Each one has a worked solution and a mark scheme showing where the marks go.

2.2.2 Scatter diagrams and correlation

Question bank

2.2.2 Scatter diagrams and correlation

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Question 5

The number of bacteria, $N$ , in a colony is recorded $t\,$ hours after an experiment begins.

The data are coded using the changes of variable $x = t$ and $y = \log_{10} N$ .

The regression line of $y\,$ on $x\,$ is found to be

$y = 2.10 + 0.18 x$

[3]

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

[1]

Explain why this model is unlikely to be reliable for predicting the number of bacteria one week after the experiment begins.

[1]

Markscheme

2.2.2 Scatter diagrams and correlation Questions

A Level
Maths
2.2.2 Scatter diagrams and correlation

157 exam-style questions on AQA A Level Maths 2.2.2 Scatter diagrams and correlation. Each one has a worked solution and a mark scheme showing where the marks go.