Integral Applications
Name:
You must show your work for all calculations using proper notation
at all times to receive full credit.
1. From 1970 to 1980, the rate of potato consumption in a given country was C(t) = 2.2 + 1.1t millions of
bushels per year, with t being years since January 1, 1970. How many bushels were consumed between
January 1, 1975 and December 31, 1979?
2. Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per
minute. The traffic flow at a particular intersection is modeled by the function F defined by
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F(t) = 82 + 4sin ç ÷ for 0 £ t £ 30 ,
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where F(t) is measured in cars per minute and t is measure in minutes.
a) To the nearest whole number, how many cars pass through the intersection over the 30-minute period?
b) Is the traffic flow increasing or decreasing at t = 7? Give a reason for your answer.
c) What is the average value of the traffic flow over the time interval 10 £ t £15? Indicate units of
measure.
d) What is the average rate of change of the traffic flow over the time interval 10 £ t £15? Indicate units of
measure.
3. A car travels along a straight road for 30 seconds starting at time t=0. Its acceleration, in ft/sec2, is given
by the linear graph below, for 0<t<30. At t=0, the velocity of the car is 0 and its position is 12.
(a) Give the equations for acceleration a(t), velocity v(t), and
position x(t) of the car at time t.
(b) What is the velocity of the car when t=6? Indicate units of
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measure.
(c) At what time t does the car reach its maximum velocity?
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Justify your answer.
(d) What is the position of the car when t=18?
(e) What is the total distance the car travels in this 30 second
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interval? Justify your answer.
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