When \(\ln y\) is plotted against \(x^2\), a straight line is obtained which passes through the points \((0.2,2.4)\) and \((0.8,0.9)\).

(i) Express \(\ln y\) in terms of \(x^2\).

(ii) Hence express \(y\) in terms of \(z\), where \(z=e^{x^2}\).