A Close Match

I was delighted to receive this solution from Niharika Paul, one of our younger solvers.

The actual functions plotted were as follows:

Two functions $f(x)$ and $g(x)$ were plotted on the same axes, where

$$f(x) =\left(\frac{20}{x}\right)^x\quad \quad g(x) = 1568\exp\left(-\frac{(x-7.3576)^2}{17.6232}\right)$$
The coefficients in $g(x)$ were chosen so as to make the function $g(x)$ match $f(x)$ as closely as possible for points past the maximum of $f(x)$

Their charts at various points are