What does $\int_{2}^{4} r(t) d t$ represent?
Choose 1 answer:
A) The average rate at which the population grew between the second and the fourth year.
(B) The change in number of people between the second and the fourth year.
(c) The time it took for the town to grow from a population of 2 people to a population of 4 people.
(D) The number of people in the town on the fourth year.

Question

What does $\int_{2}^{4} r(t) d t$ represent?
Choose 1 answer:
A) The average rate at which the population grew between the second and the fourth year.
(B) The change in number of people between the second and the fourth year.
(c) The time it took for the town to grow from a population of 2 people to a population of 4 people.
(D) The number of people in the town on the fourth year.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ The integral $\int_{2}^{4} r(t) dt$ represents the accumulation of the rate of change of a quantity, $r(t)$, from time $t=2$ to time $t=4$. ‖ ‖ step 2 ⋮ In the context of a population, $r(t)$ would represent the rate of change of the population at time $t$. ‖ ‖ step 3 ⋮ Therefore, the integral $\int_{2}^{4} r(t) dt$ calculates the total change in population from the second year to the fourth year. ‖ ***B*** ∻Key Concept∻ ⚹Definite Integral as Accumulation⚹ ∻Explanation∻ ⚹The definite integral of a rate of change function over an interval gives the total change in the quantity over that interval.⚹◊What is the relationship between the rate of change in the population and the population itself?⍭ Generate me a similar question◊

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