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 $\log_{10} y = 0.6 + 0.4x$ .
(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
2
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
3
A population $P$ after $t$ years is modelled by the regression line $\log_{10} P = 2 + 0.05t$ .
(a) Express $P$ in the form $P = ab^t$ , giving the constants to 3 s.f.
(b) State the initial population.
Level 3 · 3 marksTry it
4
The regression line of $\log_{10} y$ on $x$ has gradient $0.15$ and intercept $0.8$ .
(a) Find $a$ and $b$ so that $y = ab^x$ , to 3 s.f.
(b) Estimate $y$ when $x = 10$ .
Level 3 · 4 marksTry it
5
The braking distance $d$ of a car at speed $t$ is modelled by $\log_{10} d = 0.7 + 0.5\log_{10} t$ .
(a) Show that $d = a\,t^{n}$ , stating $a$ (3 s.f.) and $n$ .
(b) Estimate $d$ when $t = 4$ .
Level 3 · 4 marksTry it

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