An experiment was carried out recording values of \(y\) for certain values of \(x\). The variables \(x\) and \(y\) are thought to be connected by the relationship

\(y=ax^n,\)

where \(a\) and \(n\) are constants.

(i) Transform the relationship \(y=ax^n\) into straight line form.

The values of \(\ln y\) and \(\ln x\) were plotted and a line of best fit drawn.

(ii) Use the graph to find the value of \(a\) and of \(n\), stating the coordinates of the points that you use.

(iii) Find the value of \(x\) when \(y=50\).