Transportation engineers use traffic flow data to design the timing of traffic lights at intersections. At a certain intersection, the traffic flow, F(t), is modeled by the function

Question

F(t)=82+4sin(t/2) when 0¡Üt¡Ü30 minutes, where F(t), in vehicles per minute, is the rate at which vehicles pass through the intersection.

a) How many vehicles (to the nearest whole number) pass through the intersection over the 30-minute period?
b) Is the traffic flow increasing or decreasing at t=7? Include a reason with your answer
c) What is the average value of the traffic flow durign the 30-minute time period?
d) What is the average rate of change of the traffic flow during the 30-minute time period?

Answer 1

Hannah, please use Western ISO8859-1 encoding when you post mathematical symbols. It would be much easier for everyone. Thanks.

When appropriate encoding is used, the second paragraph reads:

F(t)=82+4sin(t/2) when 0≤t≤30 minutes, where F(t), in vehicles per minute, is the rate at which vehicles pass through the intersection.