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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 t t is time in years).\newlineWhat does ∫24r(t)dt \int_{2}^{4} r(t) d t 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 t t is time in years).\newlineWhat does ∫24r(t)dt \int_{2}^{4} r(t) d t 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. Given Rate of Growth: We are given the rate of population growth r(t)r(t) people per year and asked to interpret the meaning of the integral from 22 to 44 of r(t) dtr(t) \, dt. The integral of a rate function over an interval gives the total accumulation over that interval.
  2. Interpret Integral Meaning: To understand what the integral represents, we need to recall that the integral of a rate of change gives the net change over the interval. In this case, the integral from 22 to 44 of r(t) dtr(t) \, dt represents the total change in population from year 22 to year 44.
  3. Analyze Answer Choices: Now we look at the answer choices to determine which one correctly describes the integral from 22 to 44 of r(t) dtr(t) \, dt.
    (A) The average rate at which the population grew between the second and the fourth year. This is incorrect because the integral gives the total change, not the average rate.
    (B) The change in number of people between the second and the fourth year. This is the correct interpretation of the integral.
    (C) The number of people in the town on the fourth year. This is incorrect because the integral does not give the total population, but the change in population over a period.
    (D) The time it took for the town to grow from a population of 22 people to a population of 44 people. This is incorrect because the integral does not represent time, but the change in population.

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