\(r \propto \frac{1}{A}\)
\(\frac{{{r_1}}}{{{r_2}}}\, = \frac{{{A_2}}}{{{A_1}}} \)
\(⇒A_2 = A_1 \,\left( {\frac{{{r_1}}}{{{r_2}}}} \right) = A \,\left( {\frac{1}{2}} \right) = A/2\)
$(a)$ $\left(x^2-v t\right)^2$
$(b)$ $\log \left[\frac{(x+v t)}{x_0}\right]$
$(c)$ $e^{\left\{-\frac{(x+v t)}{x_0}\right\}^2}$
$(d)$ $\frac{1}{x+v t}$