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AP Calculus BC Free Response Questions
AP Calculus BC Free Response Questions Problem #2

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The rate at which people enter an amusement park on a given day is modeled by the function E defined by E(t) = 15600/(t^2 - 24t + 160).  The rate at which people leave the same amusement park on the same day is modeled by the function L defined by L(t) = 9890/(t^2 - 38t + 370).  Both E(t) and L(t) are measured in people per hour and time t is measured in hours after midnight.  These functions are valid from 9 less than or equal to t less than or equal to 23, the hours  during which the park is open.  At time t = 9, there are no people in the park.
 
(a) How many people have entered the park by 5:00 PM (t = 17)? Round your answer to the nearest whole number.
 
(b) The price of admission to the park is $15 unti 5:00PM (t = 17). After 5:00PM, the price of admission to the park is $11.  How many dollars are collected from the admissions to the park on the given day? Round your answer to the nearest whole number.
 
(c) Let H(t) = the integral from 9 to t E(x) - L(x) dx for 9 less than or equal to t less than or equal to 23. The value of H(17) to the nearest whole number is 3725. Find the value of H^1(17), and explain hte meaning of H(17) and H^1(17) in the context of the amusement park.
 
(d) At what time t, for 9 less than or equal to t less than or equal to 23, does the model predict that the number of people in the park is a maximum?

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I liked this one, i knew how to do it, it was fairly easy.