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The population of a town grows at a rate of r(t) people per year (where t is time in years). What does int_(2)^(4)r(t)dt 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 number of people in the town on the fourth year. (D) The time it took for the town to grow from a population of 2 people to a population of 4 people.

The population of a town grows at a rate of r(t)r(t) people per year (where tt is time in years). \newlineWhat does ∫24r(t) dt\int_{2}^{4}r(t)\,dt represent? \newlineChoose 11 answer:\newline(A) The average rate at which the population grew between the second and the fourth year.\newline(B) The change in number of people between the second and the fourth year.\newline(C) The number of people in the town on the fourth year.\newline(D) The time it took for the town to grow from a population of 22 people to a population of 44 people.

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Q. The population of a town grows at a rate of r(t)r(t) people per year (where tt is time in years). \newlineWhat does ∫24r(t) dt\int_{2}^{4}r(t)\,dt represent? \newlineChoose 11 answer:\newline(A) The average rate at which the population grew between the second and the fourth year.\newline(B) The change in number of people between the second and the fourth year.\newline(C) The number of people in the town on the fourth year.\newline(D) The time it took for the town to grow from a population of 22 people to a population of 44 people.
  1. Rate Function Integral: The integral of a rate function over an interval gives the total change over that interval.
  2. Total Change Calculation: So, ∫24r(t)dt\int_{2}^{4}r(t)dt calculates the total change in population from year 22 to year 44.
  3. Population Change Interpretation: This means the integral represents the change in the number of people between the 2nd2^{\text{nd}} and the 4th4^{\text{th}} year.

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