The table gives rounded values modelled by \(y=ax^n\), where \(a>0\).
\(x\)
1
2
4
8
16
\(y\)
2
5.66
16
45.3
128
On separate graph paper, plot \(\lg y\) against \(\lg x\). Estimate \(a\) and \(n\).[4]
On the same axes, draw another straight line to find the positive value of \(x\) for which \(ax^n=64/x\). State the equation of the additional line in terms of \(X=\lg x\) and \(Y=\lg y\).[4]
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