A-level · Data presentation

Exponential models and regressionExam-style questions

Fitting y = ab^x and y = ax^n to data by taking logs to get a straight line, then reading the constants off a regression line of log y on x (or on log x), and using the model to predict.

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15 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3

1
The regression line of $\log_{10} y$ on $x$ is $\log_{10} y = 0.3 + 0.2x$ . Express $y$ in terms of $x$ , giving the constants to 3 significant figures.
Level 2 · 2 marksTry it
2
Using the model $\log_{10} y = 0.3 + 0.2x$ , estimate the value of $y$ when $x = 5$ .
Level 2 · 2 marksTry it
3
The regression line of $\log_{10} y$ on $x$ is $\log_{10} y = 0.5 + 0.3x$ .

Express the model in the form $y = ab^{x}$ , giving $a$ and $b$ to 3 significant figures. (3 marks)
Level 2 · 3 marksTry it
4
The regression line of $\log_{10} y$ on $x$ is $\log_{10} y = 0.6 + 0.4x$ .
(a) Express $y$ in the form $y = ab^x$ , giving $a$ and $b$ to 3 s.f.
(b) Hence estimate $y$ when $x = 3$ .
Level 3 · 4 marksTry it
5
The regression line of $\log_{10} y$ on $\log_{10} x$ is $\log_{10} y = 0.5 + 1.5\log_{10} x$ . Express $y$ in the form $y = ax^n$ , giving the constants to 3 s.f.
Level 3 · 2 marksTry it

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