A traffic engineer monitors the rate at which cars enter a freeway onramp during rush hour. From her data, she estimates that between 4:30pm and 5:30pm the rate R(t) at which cars enter is given by:

Question

R(t)= 100(1-0.00012t^2)
car per min., where t is time in min. since 4:30.

a. find the average rate, in cars per min, at which cars enter the highway the 1st half hour.
b. find the average wight, in cars per min., at which cars enter the highway during the 2nd 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 min. assume no cars initially.

Answer 1

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