Variables \(x\) and \(y\) are such that when \(y^2\) is plotted against \(e^{2x}\), a straight line is obtained which passes through the points \((1.5,5.5)\) and \((3.7,12.1)\).

Find

(i) \(y\) in terms of \(e^{2x}\),

(ii) the value of \(y\) when \(x=3\),

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