7. The rate at which people enter an amusement park on a given day is modeled by the function E defined by E(t) =7 15600 (12 -24t+160) The rate at which people leave the same amusement park on the same day is 9890 modeled by the function L defined by L(t) = (12 - 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 for 9 s t s 23, the hours during which the park is open. At time t =9, there are no people in the park. The use of your calculator is necessary. Little to no algebraic work is needed for this problem. (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 until 5:00 pm (t = 17). After 5:00 pm, the price of admission to the park is $11. How many dollars are collected from admission to the park on the given day? Round your answer to the nearest dollar. (c) Let H(t) = [(E(t) - L(t) )dt for 9 sts 23. The value of H(17) to the nearest whole number is 3725. Find the value of H'(17), and explain the meaning of H(17) and H'(17) in the context of the amusement park. (d) At what time t, for 9 s t s 23, does the model predict that the number of people in the park is a maximum?7. The rate at which people enter an amusement park on a given day is modeled by the function E defined by E(t) =7 15600 (12 -24t+160) The rate at which people leave the same amusement park on the same day is 9890 modeled by the function L defined by L(t) = (12 - 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 for 9 s t s 23, the hours during which the park is open. At time t =9, there are no people in the park. The use of your calculator is necessary. Little to no algebraic work is needed for this problem. (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 until 5:00 pm (t = 17). After 5:00 pm, the price of admission to the park is $11. How many dollars are collected from admission to the park on the given day? Round your answer to the nearest dollar. (c) Let H(t) = [(E(t) - L(t) )dt for 9 sts 23. The value of H(17) to the nearest whole number is 3725. Find the value of H'(17), and explain the meaning of H(17) and H'(17) in the context of the amusement park. (d) At what time t, for 9 s t s 23, does the model predict that the number of people in the park is a maximum