1.20: Linear law: $\lg y$ against $x^{2}$

It is known that $y = A \times 10^{bx^{2}}$, where $A$ and $b$ are constants. When $\lg y$ is plotted against $x^{2}$, a straight line passing through the points $(3.63, 5.25)$ and $(4.83, 6.88)$ is obtained.