Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 01 (c)/Solution 1

Writing the total number of salmon that have passed through the station up until time $t$ as $Q(t)=\underset{a}{\overset{t}{\int }}q(s)ds$, we see that the rate at which salmon pass through the station at time $t$ should be given $\frac{dQ}{dt}$. But by the fundamental theorem of calculus, $\frac{dQ}{dt}=q(t)$, so the answer must be D.