Answer
The $11$th month (November) of the year
Work Step by Step
Given \begin{equation}
P(m)=10.3+2 \sqrt{m}.
\end{equation} Set $P(m)= 17$ and solve for $m$.
\begin{equation}
\begin{aligned}
P(m)&=17\\
10.3+2 \sqrt{m}& =17\\
\sqrt{m}&=\frac{17-10.3}{2}\\
\left( \sqrt{m} \right)^{2}&=\left( 3.35 \right)^{2}\\
m&\approx 11.
\end{aligned}
\end{equation} Big Jim's Mart will have a profit of $\$17000$ in the $11$th month (November) of the year.
