well, as far as I can tell, is just an "average rate of change" issue, which is just a slope value
so, at 8am, t=0, 11am is 3hrs later, so t = 3
so in short, what's the average rate from 8-11am or for t = 0 to t=3?
well [tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ f(t_2)}}-{{ f(t_1)}}}{{{ t_2}}-{{ t_1}}}\impliedby
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}
\\\\\\
%q(t)=1200+2000t−300t^2
q(t)=1200+2000t-300t^2\qquad
\begin{cases}
t_1=0\\
t_2=3
\end{cases}\implies \cfrac{f(3)-f(0)}{3-0}
\\\\\\
\cfrac{4500-1200}{3}[/tex]
