Answer
$7.2$ hours
$622$ per $100,000$ males
Work Step by Step
The quadratic function
$$f(x)=104.5x^2-1501.5x+6016$$
has positive leading coefficient, therefore its graph is a parabola that opens upward and has a minimum in the vertex.
Bring the function to the vertex form $f(x)=a(x-h)^2+k$:
$$\begin{align*}
f(x)&=104.5x^2-1501.5x+6016\\
&\approx 104.5(x^2-14.4x)+6016\\
&=104.5(x^2-14.3684x+7.1842^2)-104.5(7.18422^2)+6016\\
&\approx104.5(x-7.1842)^2+622.47\\
&\approx 104.5(x-7.2)^2+622.
\end{align*}$$
Identify the constants $a$, $h$, $k$:
$$\begin{align*}
a&=104.5\\
h&=7.2\\
k&=622.
\end{align*}$$
Determine the vertex of the function:
$$(h,k)=(7.2,622).$$
So the number of hours which correspond to the minimum death rate is $7.2$, while the minimum death rate is $622$ per $100,000$ males.
