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388 Chapter 7 Applications of Definite Integrals<br />
Standardized Test Questions<br />
You may use a graphing calculator to solve the following<br />
problems.<br />
31. True or False The figure below shows the velocity for a particle<br />
moving along the x-axis. The displacement for this particle is<br />
negative. Justify your answer. False. The displacement is the<br />
integral of the velocity from t 0 to t 5 and is positive.<br />
2<br />
1<br />
32. True or False If the velocity of a particle moving along the<br />
x-axis is always positive, then the displacement is equal to the<br />
total distance traveled. Justify your answer.<br />
33. Multiple Choice The graph below shows the rate at which<br />
water is pumped from a storage tank. Approximate the total<br />
gallons of water pumped from the tank in 24 hours. C<br />
(A) 600 (B) 2400 (C) 3600 (D) 4200 (E) 4800<br />
250<br />
200<br />
150<br />
100<br />
v (m/sec)<br />
0 1<br />
–1<br />
–2<br />
50<br />
r (gal/hr)<br />
2 3 4 5<br />
0 6 12 18 24<br />
t (sec)<br />
t (hr)<br />
34. Multiple Choice The data for the acceleration a(t) of a car<br />
from 0 to 15 seconds are given in the table below. If the velocity<br />
at t 0 is 5 ft/sec, which of the following gives the approximate<br />
velocity at t 15 using the Trapezoidal Rule? D<br />
(A) 47 ft/sec (B) 52 ft/sec (C) 120 ft/sec<br />
(D) 125 ft/sec (E) 141 ft/sec<br />
t (sec) 0 3 6 9 12 15<br />
a(t) (ftsec 2 ) 4 8 6 9 10 10<br />
35. Multiple Choice The rate at which customers arrive at a<br />
counter to be served is modeled by the function F defined by<br />
F(t) 12 6 cos <br />
p<br />
t for 0 t 60, where F(t) is measured in<br />
customers per minute and t is measured in minutes. To the nearest<br />
whole number, how many customers arrive at the counter<br />
over the 60-minute period? B<br />
(A) 720 (B) 725 (C) 732 (D) 744 (E) 756<br />
6<br />
36. Multiple Choice Pollution is being removed from a lake at a<br />
rate modeled by the function y 20e 0.5t tons/yr, where t is the<br />
number of years since 1995. Estimate the amount of pollution removed<br />
from the lake between 1995 and 2005. Round your answer<br />
to the nearest ton. A<br />
(A) 40 (B) 47 (C) 56 (D) 61 (E) 71<br />
Extending the Ideas<br />
37. Inflation Although the economy is continuously changing,<br />
we analyze it with discrete measurements. The following table<br />
records the annual inflation rate as measured each month for<br />
13 consecutive months. Use the Trapezoidal Rule with n 12<br />
to find the overall inflation rate for the year. 0.04875<br />
Month<br />
Annual Rate<br />
January 0.04<br />
February 0.04<br />
March 0.05<br />
April 0.06<br />
May 0.05<br />
June 0.04<br />
July 0.04<br />
August 0.05<br />
September 0.04<br />
October 0.06<br />
November 0.06<br />
December 0.05<br />
January 0.05<br />
38. Inflation Rate The table below shows the monthly inflation<br />
rate (in thousandths) for energy prices for thirteen consecutive<br />
months. Use the Trapezoidal Rule with n 12 to approximate<br />
the annual inflation rate for the 12-month period running<br />
from the middle of the first month to the middle of the last<br />
month. 40 thousandths or 0.040<br />
Monthly Rate<br />
Month (in thousandths)<br />
January 3.6<br />
February 4.0<br />
March 3.1<br />
April 2.8<br />
May 2.8<br />
June 3.2<br />
July 3.3<br />
August 3.1<br />
September 3.2<br />
October 3.4<br />
November 3.4<br />
December 3.9<br />
January 4.0<br />
32. True. Since the velocity is positive, the integral of the velocity is equal to<br />
the integral of its absolute value, which is the total distance traveled.