Question

A traffic engineer monitors the rate at which cars enter a freeway onramp during rush hour. From her data, she estimates that between 4:30 pm and 5:30 pm, the rate R(t) at which cars enter is given by:
R(t)=100(1-0.00012t^2)
cars per minute, where t is time in minutes since 4:30 pm.
A) find the average rate in cars per minute, at which cars enter the highway during the first half hour.
B) find the average rate, in cars per minute, at which cars enter the highway during the second half hour.
C) find the total number of cars that enter the highway during that hour.
D) cars also exit the freeway at a rate of:
E(t)=50(1-e^-t)
find the total number of cars on the highway for the first 30 minutes. Assume no cars initially.