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 defind 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 for 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 p.m. (17=t, military time)?
b.) The price of admission to the park is $15 until 5:00 p.m. (17=t). After 5:00 p.m., the price of admission to the park is $11. How many dollars are collectd from admissions to the park on the given day?
*Note- ~ is integral sign.
c.) Let H(t) = 9~t (t is upper limit) (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'(17) and explain the meaning of H(17) and H'(17) in regards to the context of the 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 nubmer of people in the park is a maximum?
Help.... please!
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 defind 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 for 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 p.m. (17=t, military time)?
b.) The price of admission to the park is $15 until 5:00 p.m. (17=t). After 5:00 p.m., the price of admission to the park is $11. How many dollars are collectd from admissions to the park on the given day?
*Note- ~ is integral sign.
c.) Let H(t) = 9~t (t is upper limit) (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'(17) and explain the meaning of H(17) and H'(17) in regards to the context of the 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 nubmer of people in the park is a maximum?
Help.... please!
