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 ∫810r′(t)dt=7 mean?Choose 1 answer:(A) As of month 10 , the magazine had 7 subscribers.(B) The average rate of change in subscribers between month 8 and month 10 was 7 subscribers per month.(C) The number of subscribers increased by 7 between t=8 and t=10 months.(D) The rate of change of number of subscribers increased by 7 subscribers per month between t=8 and t=10 months.
Q. 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 ∫810r′(t)dt=7 mean?Choose 1 answer:(A) As of month 10 , the magazine had 7 subscribers.(B) The average rate of change in subscribers between month 8 and month 10 was 7 subscribers per month.(C) The number of subscribers increased by 7 between t=8 and t=10 months.(D) The rate of change of number of subscribers increased by 7 subscribers per month between t=8 and t=10 months.
Understand the expression: Understand the integral expression.The integral of r′(t) from 8 to 10 represents the total change in the number of subscribers from month 8 to month 10.
Interpret the result: Interpret the result of the integral.Since the integral of the rate of change of subscribers, r′(t), over the interval from t=8 to t=10 is equal to 7, this means that the total change in the number of subscribers over these two months is 7 subscribers.
Match interpretation to options: Match the interpretation to the given options.The correct interpretation of the integral result is that the number of subscribers increased by 7 between t=8 and t=10 months. This matches option (C).
Eliminate incorrect options: Eliminate other options based on the interpretation.Option (A) is incorrect because the integral does not provide information about the total number of subscribers at any point in time.Option (B) is incorrect because the integral gives the total change, not the average rate of change.Option (D) is incorrect because the integral gives the total change in subscribers, not the change in the rate of change.
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