
RIshi G. answered 02/28/23
North Carolina State University Grad For Math and Science Tutoring
To find the number of cars that pass through the intersection between 6 am to 8 am, we need to integrate the traffic flow rate function, r(t), over the time interval [0, 2]. This will give us the total number of cars that pass through the intersection during the two-hour period.
The integral of r(t) with respect to t is:
∫[0,2] r(t) dt = [500t + 400t^2 - 70t^3/3] from 0 to 2
Evaluating the integral at the upper and lower limits, we get:
[500(2) + 400(2^2) - 70(2^3)/3] - [500(0) + 400(0^2) - 70(0^3)/3]
= 1000 + 1600 - (560/3)
= 2039.33
Therefore, approximately 2039 cars pass through the intersection between 6 am to 8 am.