When \(e^y\) is plotted against \(\frac1x\), a straight line graph passing through the points \((2,20)\) and \((4,8)\) is obtained.

(i) Find \(y\) in terms of \(x\).

(ii) Hence find the positive values of \(x\) for which \(y\) is defined.

(iii) Find the exact value of \(y\) when \(x=3\).

(iv) Find the exact value of \(x\) when \(y=2\).