When \(\lg y\) is plotted against \(x^2\), a straight line is obtained which passes through the points \((4,3)\) and \((12,7)\).

(i) Find the gradient of the line.

(ii) Use your answer to part (i) to express \(\lg y\) in terms of \(x\).

(iii) Hence express \(y\) in terms of \(x\), giving your answer in the form \(y=A(10^b)^{x^2}\), where \(A\) and \(b\) are constants.