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AP Calculus AB Free Response Question ( 2009 #2)

AP Calculus AB Free Response Question ( 2009 #2). By Anug Saha. Question:. Part A. Finding the integral of the rate at which people enter the concert will give you the amount of people in the auditorium at the given time. Yˌ= R(t)= 1380t²-675t³. Part B.

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AP Calculus AB Free Response Question ( 2009 #2)

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  1. AP Calculus AB Free Response Question ( 2009 #2) By Anug Saha

  2. Question:

  3. Part A Finding the integral of the rate at which people enter the concert will give you the amount of people in the auditorium at the given time. Yˌ= R(t)= 1380t²-675t³

  4. Part B To find the maximum rate at which people will be entering the auditorium you would find the derivative of R(t). R’(t)= 2760t- 2025t² Solve for zeros to find critical points So the maximum rate may occur at 0, a=1.363, or 2 The maximum rate of people coming into the auditorium occurs when t= 1.363 hours

  5. Part C The total wait time for those who enter the auditorium after time t=1 is 387.5 hours

  6. Part D The total amount of people in the room when t=2 is 980. We would divide the total wait time by the amount of people in the room to solve for how long an individual person waits in the auditorium for the concert to start. On average a person waits .776 hours for the concert to start

  7. Sources • http://apcentral.collegeboard.com/apc/public/repository/ap09_calculus_ab_sgs.pdf • http://www.youtube.com/watch?v=9RVT1mzS64Y

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