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Which graph straightens a power law y = a·xⁿ?
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All Flashcards in Topic 2.10
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2.10.18 cards
Which graph straightens a power law y = a·xⁿ?
Log-log: plot log y against log x. It's straight, with gradient n and intercept log a.
Which graph straightens an exponential law y = a·bˣ?
Semi-log: plot log y against x. It's straight, with gradient log b and intercept log a.
Why take logs of y = a·xⁿ?
log y = log a + n·log x is LINEAR in log x, so a curved power law becomes a straight line you can read.
On a log-log line for y = a·xⁿ, what is the gradient?
The power n.
On a semi-log line for y = a·bˣ, what is the gradient?
log b (so b = 10^gradient).
How do you recover a from a log-log or semi-log intercept?
The intercept is log a, so a = 10^(intercept).
How do you choose between a power and an exponential model from data?
Linearise both ways and compare R² — the fit with R² closer to 1 is straighter, so that's the model.
Semi-log gives gradient 0.3, intercept 2 for y = a·bˣ. Find a and b.
a = 10² = 100; b = 10^0.3 ≈ 2.00, so y ≈ 100·2ˣ.
Topic 2.10 study notes
Full notes & explanations for Log-log & semi-log graphs (HL only)
Math AI exam skills
Paper structures, command terms & tips
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