Linear Law - Predictions from Linearised Models

The table below shows experimental values of two variables \(x\) and \(y\).

It is known that \(x\) and \(y\) are related by the equation of the form \(y^2 = \frac{a^x}{b}\), where \(a\) and \(b\) are constants.

1. Express this equation in a form suitable for drawing a straight line graph.
2. Using a suitable scale, draw the graph for the given data and use it to estimate the value of \(a\) and of \(b\).
3. Estimate the value of \(x\) for which \(\lg \sqrt{y} = 0.7\).

Graph paper provided for plotting