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The number of subscribers to a magazine is changing at a rate of r(t) subscribers per month (where t is time in months). What does int_(8)^(10)r^(')(t)dt=7 mean? Choose 1 answer: (A) The rate of change of number of subscribers increased by 7 subscribers per month between t=8 and t=10 months. (B) As of month 10, the magazine had 7 subscribers. (C) The number of subscribers increased by 7 between t=8 and t=10 months. (D) The average rate of change in subscribers between month 8 and month 10 was 7 subscribers per month.

The number of subscribers to a magazine is changing at a rate of r(t) r(t) subscribers per month (where t t is time in months).\newlineWhat does ∫810r′(t)dt=7 \int_{8}^{10} r^{\prime}(t) d t=7 mean?\newlineChoose 11 answer:\newline(A) The rate of change of number of subscribers increased by 77 subscribers per month between t=8 t=8 and t=10 t=10 months.\newline(B) As of month 1010, the magazine had 77 subscribers.\newline(C) The number of subscribers increased by 77 between t=8 t=8 and t=10 t=10 months.\newline(D) The average rate of change in subscribers between month 88 and month 1010 was 77 subscribers per month.

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Q. The number of subscribers to a magazine is changing at a rate of r(t) r(t) subscribers per month (where t t is time in months).\newlineWhat does ∫810r′(t)dt=7 \int_{8}^{10} r^{\prime}(t) d t=7 mean?\newlineChoose 11 answer:\newline(A) The rate of change of number of subscribers increased by 77 subscribers per month between t=8 t=8 and t=10 t=10 months.\newline(B) As of month 1010, the magazine had 77 subscribers.\newline(C) The number of subscribers increased by 77 between t=8 t=8 and t=10 t=10 months.\newline(D) The average rate of change in subscribers between month 88 and month 1010 was 77 subscribers per month.
  1. Interpretation of Integral: The integral of a rate of change function over an interval gives the net change over that interval. In this case, the integral of r′(t)r'(t) from t=8t=8 to t=10t=10 represents the net change in the number of subscribers from month 88 to month 1010.
  2. Calculation of Net Change: Since the integral of r′(t)r'(t) from 88 to 1010 is equal to 77, this means that the total change in the number of subscribers over this time period is 77 subscribers.
  3. Evaluation of Answer Choices: We can now evaluate the answer choices based on the interpretation of the integral:\newline(A) This choice suggests that the rate of change increased, which is not what the integral measures.\newline(B) This choice suggests a total number of subscribers at a specific time, which is not what the integral measures.\newline(C) This choice correctly interprets the integral as the net increase in the number of subscribers over the time interval.\newline(D) This choice suggests an average rate of change, which is not what the integral measures.
  4. Correct Answer Explanation: Based on the above reasoning, the correct answer is (C) The number of subscribers increased by 77 between t=8t=8 and t=10t=10 months.

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