Answer
The equilibrium point between the price of supply and demand for sale of stereos is$\left( 6,\$403\right)$.
Work Step by Step
The equation of supply price is $S\left( x \right)={{e}^{x}}$, and the equation of demanded price is $D\left( x \right)=162,755{{e}^{-x}}$
We find:
$\begin{align}
& S\left( x \right)=D\left( x \right) \\
& {{e}^{x}}=162,755{{e}^{-x}}
\end{align}$
Now, multiply by ${{e}^{x}}$ on both sides:
$\begin{align}
& {{e}^{x}}=162,755{{e}^{-x}} \\
& {{e}^{2x}}=162,755
\end{align}$
$\begin{align}
& {{e}^{2x}}=162,755 \\
& \ln {{e}^{2x}}=\ln 162,755 \\
& 2x=\ln 162,755 \\
& x=\frac{\ln 162,755}{2}
\end{align}$
Further simplified,
$\begin{align}
& x=\frac{\ln 162,755}{2} \\
& x=\frac{12.0}{2} \\
& x=6
\end{align}$
Now, to find second coordinate of equilibrium, put the value of $x=6$in $S\left( x \right)$ as,
$\begin{align}
& S\left( x \right)={{e}^{x}} \\
& S\left( 6 \right)={{e}^{6}} \\
& S\left( x \right)\approx 403
\end{align}$
