A student is investigating a family of similar shapes. She measures the width, w, and the area,

Question:

A student is investigating a family of similar shapes. She measures the width, w, and the area, A, of each shape. She suspects there is a formula of the form A = pwq, so she plots the logarithms of her results.


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The graph has a gradient of 2 and passes through −0.1049 on the vertical axis.


a. Write down an equation for the line.


b. Starting with your answer to part a, or otherwise, find the exact value of q and the value of p to 4 decimal places.


c. Suggest the name of the family of shapes that the student is investigating, and justify your answer.

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