2025 IGCSE Additional Mathematics October/November 0606/23 Q9

6 marks

Two variables, \(x\) and \(y\), are related by an equation of the form \(y=Ax^b\), where \(A\) and \(b\) are constants.

The following pairs of values of \(x\) and \(y\) are given.

\(x\)	0.61	4.48	12.18	33.1
\(y\)	1.65	4.47	7.39	12.17

On the axes below, use these values to draw the straight-line graph of \(\ln y\) against \(\ln x\).[2]
Use your graph to find the values of \(A\) and \(b\).[4]

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Answer:(a) Graph shown. (b) \(A\approx2.12,\ b\approx0.50\).

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