A large flea market is held at a local fairgrounds on the first Saturday of each month. The rates at which people enter and leave the flea market are recorded for a three hour period beginning at 12 noon. The rate at which people arrive is modeled by the function A(t) 42 sin (0.03 t-07) + 71. The function L(t) = 42 sin (0.034 t-1.52) + 42 models the rate at which people leave the fairgrounds. Both A(t) and L(t) are measured in people per minute and t is measured for 0 t 180 minutes, when the count begins at t 0, there are already 1572 people in the flea market area of the fairgrounds. Answer all parts in complete sentences including units a) How many additional people arrive for the flea market during the 3-hour period after it opens to the public?
b) Write an expression for P(t), the total number of people at the flea market at time t.
c) Find the value of P (75) and explain its meaning.