The table shows the variables \(x\) and \(y\) which are related by the equation \(y=A b^{x^{2}}\), where \(A\) and \(b\) are constants.

(a) Use the data to draw a straight line graph of \(\ln y\) against \(x^{2}\). (b) Use your graph to estimate the values of \(A\) and \(b\). Give your answers correct to 1 significant figure. (c) Use your graph to estimate the value of \(x\) when \(y=200\). Give your answer correct to 2 significant figures.