Mathematics 9709 · AS & A Level · Logarithmic and exponential functions

Logarithmic and exponential functions — practice question

The variables $x$ and $y$ are linked by the equation $y^n = Ax^3$, with $n$ and $A$ constant. It is stated that $y = 2.58$ when $x = 1.20$, and $y = 9.49$ when $x = 2.51$.
(i)[2]

Explain why plotting $\ln y$ against $\ln x$ gives a straight line.

(ii)[4]

Determine the values of $n$ and $A$, with answers accurate to 2 decimal places.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: State or show $n\ln y=\ln A+3\ln x$

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