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

A certain population of wild salmon swims upstream, past a research station. A biologist keeps track of how many individual salmon pass the station over time. Suppose $\int_{a}^{b} q (t) d t$ gives the number of salmon that passed from time $t = a$ to time $t = b$ , where $t$ is measured in hours. Select the best interpretation of $q (t)$ from the list below.

A: $q (t)$ gives the total distance (measured in kilometres) the salmon have travelled from time $t = a$ to time $t = b$ .

B: $q (t)$ gives the acceleration of the salmon, from time $t = a$ to time $t = b$ .

C: $q (t)$ gives the number of salmon that passed the station from time $t = a$ to time $t = b$ , where $t$ is measured in hours.

D: $q (t)$ gives the rate (in number of salmon per hour) at which salmon pass the research station at time $t$ .

E: $q (t)$ gives the rate (in kilometres per hour) at which salmon pass the research station at time $t$ .

F: $q (t)$ gives the rate of change (in salmon per hour per hour, $\frac{salmon}{{hour}^{2}}$ ) of the rate at which salmon are passing the research station.