A)
B)
C)
D)
Answer:
D
52)
Graph the following example of exponential decay: y =350e–0.038t , 0 t 45, 0 y 900.
12
A)
B)
C)
D)
Answer:
C
Solve the problem.
53)
If the marginal price dp
dx at x units of demand per week is proportional to the price p, and if at $80 there is no
weekly demand [p(0) = 80], and if at $50.18 there is a weekly demand of 8 units [p(8) = 50.18], find the
price–demand equation.
A)
p(x) = 4.38e0.305x
B)
p(x) = 4.38e–0.058x
C)
D)
p(x) = 80e–0.058x
Answer:
D
54)
Find the amount A in an account (to the nearest dollar) after 5 years if dA
dt = rA, A(0) = 800, and A(10) = 1800.
A)
$1000
B)
$1200
C)
D)
$1100
Answer:
B
13
55)
A single injection of a drug is administered to a patient. The amount Q in the body then decreases at a rate
proportional to the amount present, and for this particular drug the rate is 3% per hour. Thus, dQ
dt = – 0.03Q
with Q(0) =Q0, where t is time in hours. If the initial injection is 4 milliliters [Q(0) = 4], about how many hours
after the drug is given will there be 2 milliliters of the drug remaining in the body? (Round answer to the
nearest tenth of an hour.)
A)
21.3 hours
B)
11.3 hours
C)
D)
69.3 hours
Answer:
C
56)
At the beginning of an advertising campaign for a new product in a city of 500,000 people, no one is aware of
the product. After 10 days, 100,000 people are aware of the product. If N = N(t) is the number of people (in
thousands) who are aware of the product t days after the beginning of the advertising campaign, solve the
following differential equation for N(t):
dN
dt = k(500 – N); N(0) = 0; N(10) = 100.
A)
N(t) = 500(e–0.022t – 1)
B)
N(t) = 500(e0.022t – 1)
C)
N(t) = 500(1 –e–0.022t)
D)
N(t) = 500(1 –e0.022t)
Answer:
C
Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.
57)
A)
right rectangles
B)
left rectangles
C)
neither
Answer:
B
14
58)
A)
right rectangles
B)
left rectangles
C)
neither
Answer:
C
59)
A)
neither
B)
right rectangles
C)
left rectangles
Answer:
B
60)
A)
left rectangles
B)
neither
C)
right rectangles
Answer:
A
15
Provide an appropriate response.
61)
Divide the interval [0, 8] into four equal subintervals and draw in the corresponding left rectangles.
A)
B)
C)
D)
Answer:
C
16
62)
Divide the interval [0, 8] into four equal subintervals and draw in the corresponding right rectangles.
A)
B)
C)
D)
Answer:
C
Approximate the area under the graph of f(x) and above the x–axis using n rectangles.
63)
f(x) = 2x + 3 from x = 0 to x = 2; n = 4; compute R4
A)
13
B)
11
C)
D)
17
Answer:
B
17
64)
f(x) = 3x2– 2 from x = 1 to x = 5; n = 4; compute R4
A)
144
B)
140
C)
D)
154
Answer:
D
65)
f(x) =x2+ 2; interval [0, 5]; n = 5; compute L5
A)
32
B)
40
C)
D)
66
Answer:
B
Provide an appropriate response.
66)
Calculate the Riemann sum, Sn , for the function f(x) =x2– 3x – 10 on the interval [–3, 7]. Partition [–3, 7] into
five subintervals of equal length and for each subinterval [xk–1, xk], let Ck be the midpoint.
A)
–38
B)
– 40
C)
D)
38
Answer:
B
67)
How large should n (n an integer) be chosen for Ln and Rn for the approximation of
4
1
(ln x + 1) dx to be
within 0.05 of the true value?
A)
n 42
B)
n 28
C)
D)
n 90
Answer:
D
68)
 
Given that
7
2
x dx =45
2,
5
2
x2 dx =117
3,
7
2
x2 dx =335
3,find the definite integral
7
2
(4x2– 2x) dx.
A)
2725
2
B)
– 6
C)
D)
1340
3
Answer:
C
69)
 
Given
3
1
f(x) dx = 4 and
3
1
g(x) dx = 2, use properties of definite integrals to evaluate
3
1
[2f(x) + 5g(x)] dx.
A)
24
B)
18
C)
D)
13
Answer:
B
70)
 
Given
5
3
f(x) dx = 7 and
5
3
g(x) dx = 1, find
5
3
[4f(x) – 2g(x)] dx.
A)
30
B)
28
C)
D)
26
Answer:
D
Evaluate the integral.
71)
1
–1
(3x2– 8x) dx
A)
7
B)
2
C)
D)
12
Answer:
B
18
72)
16
3
3 x dx .
A)
288
B)
192
C)
D)
128
Answer:
D
73)
b
0
9x8 dx
A)
9b9
B)
1
9b9
C)
D)
b7
Answer:
C
74)
e
1
16x –5
x dx
(Express your answer in terms for e.)
A)
8e2– 5
B)
8e2– 8
C)
D)
8e2– 13
Answer:
D
75)
0.4
0.1
5e2x dx
(Round to three decimal places.)
A)
5.021
B)
2.510
C)
D)
0.425
Answer:
B
76)
2
1
4 x –5
xdx
(Round to three decimal places.)
A)
12.846
B)
7.505
C)
D)
1.410
Answer:
D
77)
2
0
4x + 1
4x2+ 2x + 2 dx
(Round to three decimal places.)
A)
1.040
B)
1.778
C)
D)
1.199
Answer:
D
Solve the problem.
78)
A factory discharges pollutants into a large river at a rate that is estimated by a water quality control agency to
be P'(t) = t 1 +t2 for 0 t 5, where P(t) is the total number of tons of pollutants discharged into the river after t
years of operation. What quantity of pollutants will be discharged into the river from the end of the third year to
the end of the fifth year? (Round to two decimal places.)
A)
32.67 tons
B)
75.71 tons
C)
D)
50.67 tons
Answer:
C
19
79)
Test marketing for a new health–food snack product in a selected area suggests that sales (in thousands of
dollars) will increase at a rate given by S'(t) = 40 – 40e–0.16t, t months after an aggressive national advertising
campaign is begun. Find total sales during the second 12 months of the campaign. (Round to the nearest
thousand dollars.)
A)
$511,000
B)
$267,000
C)
D)
$693,000
Answer:
C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
80)
 
(A) Calculate the change in F(x) from x =1 to x =5.
(B) Graph F(x) and use geometric formulas to calculate the area between the graph of F(x) and the x–axis from
x =1 to x =5.
(C) What guarantees that your answers to (A) and (B) are equal?
F(x) = x( 3
2x +3)
Answer:
(A) 48
(B) 48
(C) The fundamental theorem of calculus
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the integral.
81)
–1
–3
(x2+ x + 6) dx
A)
28.33
B)
17.17
C)
D)
16.67
Answer:
D
82)
3
1
(2x3– 3x–2) dx
A)
46
B)
44.5
C)
D)
38
Answer:
D
20
83)
4
0
5 x dx
A)
60
B)
10
C)
D)
80
3
Answer:
D
84)
b
0
8exdx
A)
8eb– 1
B)
8eb + 1
b + 1 –e
2
C)
D)
8eb–8
Answer:
D
85)
e
1
12
xdx
A)
12
B)
–12
C)
D)
0
Answer:
A
86)
5
2
x2–16
x –4dx
A)
33
B)
33
2
C)
D)
–3
2
Answer:
C
Provide an appropriate response.
87)
Find the average value of the function g(x) =32e0.04x over the interval [10, 30]. Round your answer to two
decimal places.
A)
45.71
B)
73.13
C)
D)
2.29
Answer:
B
88)
Find the average value of the function y = 2x4 over the interval [– 2, 2].
A)
16
5
B)
128
5
C)
D)
32
5
Answer:
D
89)
Find the average value of the function y = 5 –x2 over the interval [– 3, 2].
A)
–2
3
B)
8
3
C)
D)
4
15
Answer:
B
90)
Find the average value of the function y =e–x over the interval [ 0, 3]. Express an exact answer in terms of e.
A)
e– 3 – 1
3
B)
e– 1.5
C)
D)
1 –e–3
3
Answer:
D
21
Solve the problem.
91)
The number of cheeseburgers (in thousands) sold each day by a chain of restaurants t days after the end of an
advertising campaign is given by S(t) = 9 – 10e–0.3t. What is the average number of cheeseburgers sold each day
during the first 7 days after the end of the advertising campaign?
A)
5904 cheeseburgers
B)
4770 cheeseburgers
C)
3740 cheeseburgers
D)
4821 cheeseburgers
Answer:
D
92)
A population of bacteria grows at a rate of P'(t) = 12 et where t is time in hours. Determine how much the
population increases from t = 0 to t = 3. Round your answer to two decimal places.
A)
470.06
B)
241.03
C)
D)
229.03
Answer:
D
93)
A drug is injected into the bloodstream of a patient through her right arm. The concentration of the drug, C(t)
(in milligrams per cubic centimeter), in the blood stream of the left arm t hours after the injection is given by
C(t) =0.15t
t2+ 1 . What is the average concentration of the drug in the bloodstream of the left arm during the first
two hours after the injection?
A)
0.344 milligrams per cubic centimeter
B)
0.060 milligrams per cubic centimeter
C)
0.121 milligrams per cubic centimeter
D)
0.241 milligrams per cubic centimeter
Answer:
B
22