The function s(t) gives the number of students enrolled in a school by time t (in years). What does int_(15)^(18)s^(')(t)dt=20 mean? Choose 1 answer: (A) There were 20 more students enrolled in year 18 than in year 15 . (B) Between years 15 and 18, the cumulative number of years of schooling of all of the enrolled students is 20 years. (C) There are 20 students enrolled in year 18 . (D) The rate of change of enrollment is 20 students per year more in year 18 than it was in year 15 .

Question

The function  s(t) gives the number of students enrolled in a school by time  t (in years). What does  int_(15)^(18)s^(')(t)dt=20 mean? Choose 1 answer: (A) There were 20 more students enrolled in year 18 than in year 15 . (B) Between years 15 and 18, the cumulative number of years of schooling of all of the enrolled students is 20 years. (C) There are 20 students enrolled in year 18 . (D) The rate of change of enrollment is 20 students per year more in year 18 than it was in year 15 .

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Understand Meaning of Integral: Understand the meaning of the integral of the derivative of a function. The integral of the derivative of a function over an interval gives the net change in the function's value over that interval. In this context, s(t) represents the number of students, and s'(t) is the rate of change of the number of students with respect to time. Therefore, the integral from 15 to 18 of s'(t) dt represents the net change in the number of students enrolled in the school from year 15 to year 18.Interpret Given Integral Value: Interpret the given integral value. Since int_(15)^(18)s'(t)dt = 20, this means that the net change in the number of students from year 15 to year 18 is 20 students. This does not give us information about the rate of change per year or the cumulative number of years of schooling; it simply tells us the difference in the number of students between the two years.Match Interpretation to Answer Choices: Match the interpretation to the given answer choices. Based on the interpretation in Step 2, the correct answer is that there were 20 more students enrolled in year 18 than in year 15. This matches answer choice (A) and does not match the other answer choices, as they describe different scenarios that are not supported by the integral's value.

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