It is given that \(y=A(10^{bx})\), where \(A\) and \(b\) are constants. The straight line graph obtained when \(\lg y\) is plotted against \(x\) passes through the points \((0.5,2.2)\) and \((1.0,3.7)\).

(i) Find \(A\) and \(b\).

Using your values of \(A\) and \(b\), find

(ii) the value of \(y\) when \(x=0.6\),

(iii) the value of \(x\) when \(y=600\).