Hint
Inputs and outputs of a log plot are positive. Use the two given transformed points.
Worked solution
(a)
Take base-2 logarithms of y=Axⁿ and use the power and product laws.
Answer: \(V=nU+\log_2 A\)
(b)
The slope is \(\displaystyle \frac{17- 7}{3- 1}= 5\). The intercept is 2, so \(\displaystyle A=2^2=4\).
Answer: \(4\) and \(5\)
(c)
Undo the base-2 logarithm of A.
\(4\)
Answer: \(4\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Take the stated logarithm and identify slope and intercept in U,V.
- 1 mark: Give all results requested in this part, with the correct signs, exact values, units, branch and boundary inclusion where applicable.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: The intercept is log_b A, not A.
(b) · 2 marks
- 1 mark: Find the transformed slope and intercept and reverse the intercept logarithm.
- 1 mark: Give all results requested in this part, with the correct signs, exact values, units, branch and boundary inclusion where applicable.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A power law is not linear in x and log y unless n has a different role.
(c) · 2 marks
- 1 mark: Undo the base-2 logarithm of A.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: The intercept is log_b A, not A.
Total: 6 marks.