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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). At t=3, the town's population was 1000 people. What does 1000+int_(3)^(8)r(t)dt=1500 mean? Choose 1 answer: (A) The town's population grew at a rate of 1500 people per year at t=8. (B) The town's population grew by 1500 people between t=3 and t=8. (C) The average rate at which the population grew between t=3 and t=8 is 1500 people per year. (D) At t=8, the town's population was 1500 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). At t=3 t=3 , the town's population was 10001000 people.\newlineWhat does 1000+∫38r(t)dt=1500 1000+\int_{3}^{8} r(t) d t=1500 mean?\newlineChoose 11 answer:\newline(A) The town's population grew at a rate of 15001500 people per year at t=8 t=8 .\newline(B) The town's population grew by 15001500 people between t=3 t=3 and t=8 t=8 .\newline(C) The average rate at which the population grew between t=3 t=3 and t=8 t=8 is 15001500 people per year.\newline(D) At t=8 t=8 , the town's population was 15001500 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). At t=3 t=3 , the town's population was 10001000 people.\newlineWhat does 1000+∫38r(t)dt=1500 1000+\int_{3}^{8} r(t) d t=1500 mean?\newlineChoose 11 answer:\newline(A) The town's population grew at a rate of 15001500 people per year at t=8 t=8 .\newline(B) The town's population grew by 15001500 people between t=3 t=3 and t=8 t=8 .\newline(C) The average rate at which the population grew between t=3 t=3 and t=8 t=8 is 15001500 people per year.\newline(D) At t=8 t=8 , the town's population was 15001500 people.
  1. Evaluate Integral Meaning: Evaluate the meaning of the integral in the context of population growth. The integral ∫38r(t)dt\int_{3}^{8}r(t)dt represents the total change in population from time t=3t=3 to t=8t=8.
  2. Interpret Equation: Interpret the equation 1000+∫38r(t)dt=15001000 + \int_{3}^{8}r(t)dt = 1500. The initial population at t=3t=3 is 10001000 people. The integral adds the total population change from t=3t=3 to t=8t=8 to this initial population. The result, 15001500, is the population at t=8t=8.
  3. Determine Correct Answer Choice: Determine which answer choice correctly describes the equation.\newline(A) Incorrect - The equation does not describe the rate of population growth at t=8t=8.\newline(B) Correct - The equation indicates that the population grew by 500500 people (1500−10001500 - 1000) between t=3t=3 and t=8t=8.\newline(C) Incorrect - The equation does not provide information about the average rate of growth.\newline(D) Incorrect - The equation states that the population is 15001500 at t=8t=8, not that it grew by 15001500 people.

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