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11/26/11 3:27 PM
Review problems for Test 4 (Sec 7.4 to 4.6) (2159091)
Current Score:
0/155
49 50 51 Question
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/2 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/2 0/1 0/1 0/1 0/1 0/3 0/2 0/3 0/5 0/3 0/1
Points
1.
0/2 points
Total
0/155
SPreCalc6 7.4.017. [1784223]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal
places where appropriate.)
cos ! = !
2
2
!=
rad
List six specific solutions.
!=
2.
rad
0/2 points
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SPreCalc6 7.4.018. [1784108]
-
Page 1 of 74
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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal
places where appropriate.)
cos ! = 1
2
!=
rad
List six specific solutions.
!=
3.
rad
0/2 points
SPreCalc6 7.4.019. [1784279]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal
places where appropriate.)
sin ! =
2
2
!=
rad
List six specific solutions.
!=
rad
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4.
11/26/11 3:27 PM
0/2 points
SPreCalc6 7.4.020. [1784095]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal
places where appropriate.)
sin ! = !
3
2
!=
rad
List six specific solutions.
!=
5.
rad
0/1 points
SPreCalc6 7.4.025. [1787240]
-
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to
two decimal places where appropriate.)
cos ! + 1 = 0
!=
6.
rad
0/1 points
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SPreCalc6 7.4.026. [1787243]
-
Page 3 of 74
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Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to
two decimal places where appropriate.)
sin ! + 1 = 0
!=
7.
rad
0/1 points
SPreCalc6 7.4.042. [1721910]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal
places where appropriate. If there is no solution, enter NO SOLUTION.)
2 cos2 ! ! cos ! ! 1 = 0
!=
8.
0/1 points
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SPreCalc6 7.4.045. [1721758]
-
Page 4 of 74
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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal
places where appropriate. If there is no solution, enter NO SOLUTION.)
2 cos2 ! ! 9 cos ! + 4 = 0
!=
9.
0/1 points
SPreCalc6 7.4.046. [1721939]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal
places where appropriate. If there is no solution, enter NO SOLUTION.)
sin2 ! ! 4 sin ! ! 5 = 0
!=
10.
0/1 points
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SPreCalc6 7.4.050. [1766471]
-
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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal
places where appropriate. If there is no solution, enter NO SOLUTION.)
3 tan3! = tan !
!=
11.
0/1 points
SPreCalc6 7.4.053. [1721787]
-
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal
places where appropriate. If there is no solution, enter NO SOLUTION.)
sin ! cos ! ! 9 sin ! = 0
!=
12.
0/1 points
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SPreCalc6 4.1.021. [1614324]
-
Page 6 of 74
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Find the exponential function f(x) = ax whose graph is given.
f(x) =
13.
0/1 points
SPreCalc6 4.1.023. [1614500]
-
Match the exponential function with one of the graphs labeled I or II.
f(x) = 3x + 1
I
II
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The graph of f(x) = 3x + 1 is graph I.
The graph of f(x) = 3x + 1 is graph II.
14.
0/1 points
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SPreCalc6 4.1.024. [1614497]
-
Page 8 of 74
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Match the exponential function with one of the graphs labeled I or II.
f(x) = 4x + 1
I
II
The graph of f(x) = 4x + 1 is graph I.
The graph of f(x) = 4x + 1 is graph II.
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15.
11/26/11 3:27 PM
0/4 points
SPreCalc6 4.1.028. [1697119]
-
Graph the function, not by plotting points, but by starting from the graphs below.
g(x) = 10x ! 2
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State the domain and range.
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State the domain and range.
Domain:
(! , 0)
(!2, 2)
(! ,
)
(! , 2]
[0,
)
Range:
(!2,
)
[! , 2]
(0,
[0,
(! ,
)
)
)
State the asymptote.
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16.
11/26/11 3:27 PM
0/4 points
SPreCalc6 4.1.029. [1697109]
-
Graph the function, not by plotting points, but by starting from the graphs below.
h(x) = 1 +
1 x
3
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State the domain and range.
Domain:
(!1, 1)
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(!1, 1)
(!1,
)
(! , 0]
(0,
)
(! ,
)
Range:
(! ,
)
(1,
(0,
(!1,
)
)
)
(! , 0]
State the asymptote.
17.
0/4 points
SPreCalc6 4.1.031.MI. [1926315]
-
Graph the function, not by plotting points, but by starting from the graphs below.
f(x) = 3x + 2
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f(x) = 3x + 2
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State the domain and range.
Domain:
(! ,
)
(! , 0)
(0,
)
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(! , 2)
(2,
)
Range:
(! , 0)
(0,
)
(! , 2)
(! ,
(2,
)
)
State the asymptote.
18.
0/4 points
SPreCalc6 4.1.033. [1803752]
-
Graph the function, not by plotting points, but by starting from the graphs below.
y = 2!x + 1
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State the domain and range.
Domain:
[0,
)
(!2, 2)
(! , 0]
(! ,
)
(! , 0)
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Range:
(1,
)
(! , 0]
(!1,
)
(0, 5)
(! , 2)
State the asymptote.
19.
0/4 points
SPreCalc6 4.1.036. [1803618]
-
Graph the function, not by plotting points, but by starting from the graphs below.
h(x) = 3x ! 2 + 1
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State the domain and range.
Domain:
(! , 2]
(!2, 2)
(! , 0)
[0,
)
(! ,
)
Range:
(1,
)
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(1,
)
[! , 2]
(!2,
)
(! ,
)
[!1,
)
State the asymptote.
20.
0/4 points
SPreCalc6 4.2.008. [1697126]
-
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below.
y = 5 ! ex
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State the domain and range.
Domain:
(! , 2]
(! , 5)
(!2, 2)
(! ,
(!5,
)
)
Range:
(!5,
)
(! , 5)
(! ,
)
[!2, 2]
(! , 4]
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State the asymptote.
21.
0/4 points
SPreCalc6 4.2.011.MI. [1699134]
-
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below.
f(x) = ex ! 3
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State the domain and range.
Domain:
(!e,
(0,
)
)
(! ,
(!3,
)
)
(! , 3]
Range:
(! , 3]
(! ,
)
(!3,
)
(0,
(!e,
)
)
State the asymptote.
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22.
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0/4 points
SPreCalc6 4.2.012.MI. [1699128]
-
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below.
y = ex ! 1 + 3
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State the domain and range.
Domain:
(!3,
(3,
)
)
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(! ,
)
(! , e]
(0,
)
Range:
(3,
(0,
)
(1,
)
[0,
)
(!3,
)
)
State the asymptote.
23.
0/4 points
SPreCalc6 4.2.013. [1697098]
-
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below.
h(x) = ex + 1 ! 4
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State the domain and range.
Domain:
(! , !4)
(! ,
)
(! , 4)
(!4,
)
(!4, 4)
Range:
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(!4, 4)
(! , !4)
(!4,
)
(! , 4)
(! ,
)
State the asymptote.
24.
0/4 points
SPreCalc6 4.2.014. [1697091]
-
Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure below.
g(x) = !ex ! 1 ! 3
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State the domain and range.
Domain:
(! , !3)
(3,
)
(!3,
)
(! , 3)
(! ,
)
Range:
(!3,
(3,
)
)
(! , 3)
(! ,
)
(! , !3)
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State the asymptote.
25.
0/2 points
SPreCalc6 4.3.011. [1613828]
-
SPreCalc6 4.3.007.MI. [1615824]
-
Express the equation in exponential form.
26.
(a)
ln 8 = x
(b)
ln y = 8
0/2 points
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Express the equation in exponential form.
27.
(a)
log5 5 = 1
(b)
log5 1 = 0
0/2 points
SPreCalc6 4.3.009.MI. [1615249]
-
SPreCalc6 4.3.013.MI. [1616238]
-
Express the equation in exponential form.
28.
(a)
log9 3 = 1
2
(b)
log3 1 = !2
9
0/2 points
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Express the equation in logarithmic form.
29.
(a)
34 = 81
(b)
10!1 = 0.1
0/2 points
SPreCalc6 4.3.014.MI. [1614995]
-
SPreCalc6 4.3.017. [1616057]
-
Express the equation in logarithmic form.
30.
(a)
102 = 100
(b)
641/3 = 4
0/2 points
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Express the equation in logarithmic form.
31.
(a)
ex = 7
(b)
e2 = y
0/2 points
SPreCalc6 4.3.018. [1614404]
-
SPreCalc6 4.3.023.MI. [1615345]
-
Express the equation in logarithmic form.
32.
(a)
ex + 1 = 0.4
(b)
e0.4x = t
0/3 points
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Evaluate the expression.
(a)
log3
1
81
-4
(b)
log2 "2
1/2
(c)
log4 0.25
-1
33.
0/3 points
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SPreCalc6 4.3.025.MI. [1615729]
-
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Evaluate the expression.
34.
(a)
2log2 30
(b)
5log5 32
(c)
eln
11
0/2 points
SPreCalc6 4.3.034. [1615440]
-
SPreCalc6 4.3.035. [1613616]
-
Use the definition of the logarithmic function to find x.
(a)
logx 1000 = 3
x=
(b)
x=
35.
10
logx 25 = 2
5
0/2 points
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Use the definition of the logarithmic function to find x.
(a)
logx 8 = 3
x=
(b)
2
logx 64 = 3
2
x=
36.
16
0/4 points
SPreCalc6 4.3.053. [1613494]
-
Graph the function, not by plotting points, but by starting from the graphs in the figures below. State the domain, range, and
asymptote.
f(x) = log10(x ! 1)
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Domain:
(!10,
)
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(!10,
)
(1, 8)
(! , 0)
(1,
(! ,
)
)
Range:
(! ,
(0,
)
)
(! , 10)
(1,
)
(! , 1)
asymptote
37.
0/4 points
SPreCalc6 4.3.057. [1614338]
-
Graph the function, not by plotting points, but by starting from the graphs in the figures below. State the domain, range, and
asymptote.
y = 3 + log5 x
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y = 3 + log5 x
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Domain:
(0,
(3,
)
)
(!3,
)
(! , 4)
(! ,
)
Range:
(!2,
(0,
)
)
(! , 4)
(!2, 4)
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(!2, 4)
(! ,
)
asymptote
38.
0/4 points
SPreCalc6 4.3.058.MI. [1614168]
-
Graph the function, not by plotting points, but by starting from the graphs in the figures below. State the domain, range, and
asymptote.
y = log10(x ! 1) ! 2
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Domain:
(!1, 3)
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(!1, 3)
(0,
)
(! ,
)
(1,
(!1,
)
)
Range:
(! , 10)
(1,
)
(! ,
(0,
)
)
(! , 1)
asymptote
39.
0/4 points
SPreCalc6 4.3.059. [1614510]
-
Graph the function, not by plotting points, but by starting from the graph in the figure below. State the domain, range, and
asymptote.
y = 1 ! log3 x
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y = 1 ! log3 x
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Domain:
(!1,
)
(0,
)
(! , 0)
(1,
)
(! ,
)
Range:
(! ,
)
(! , 2)
(1,
)
(0,
)
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(!1,
)
asymptote
40.
0/4 points
SPreCalc6 4.3.060. [1615236]
-
Graph the function, not by plotting points, but by starting from the graphs in the figures below. State the domain, range, and
asymptote.
y = 3 + ln(!x)
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Domain:
(!3,
)
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(! ,
(0,
)
)
(! , 0)
(! , 4)
Range:
(0,
)
(3,
)
(! , 0)
(! ,
)
(! , 3)
asymptote
41.
0/1 points
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SPreCalc6 4.4.007. [1615599]
-
Page 56 of 74
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Evaluate the expression.
log7
343
3/2
42.
0/1 points
SPreCalc6 4.4.008.MI. [1615606]
-
SPreCalc6 4.4.023. [1615468]
-
SPreCalc6 4.4.024. [1613900]
-
Evaluate the expression.
log2 16 ! log2 2
3
43.
0/1 points
Use the Laws of Logarithms to expand the expression.
log 810
44.
0/1 points
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Use the Laws of Logarithms to expand the expression.
ln
45.
z
0/1 points
SPreCalc6 4.4.029. [1616265]
-
SPreCalc6 4.4.030.MI. [1614440]
-
Use the Laws of Logarithms to expand the expression.
log9
46.
4
x2 + 5
0/1 points
Use the Laws of Logarithms to expand the expression.
6
loga x
yz7
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47.
11/26/11 3:27 PM
0/1 points
SPreCalc6 4.4.032.MI. [1613456]
-
SPreCalc6 4.4.034. [1615487]
-
SPreCalc6 4.4.036.MI. [1613880]
-
Use the Laws of Logarithms to expand the expression.
ln
48.
3
7r6s
0/1 points
Use the Laws of Logarithms to expand the expression.
log
49.
a4
b2
c
0/1 points
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Use the Laws of Logarithms to expand the expression.
log7
50.
x!8
x+8
0/1 points
SPreCalc6 4.4.038. [1615198]
-
SPreCalc6 4.4.043. [1616226]
-
Use the Laws of Logarithms to expand the expression.
ln
51.
6x5
(x + 3)5
0/1 points
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Use the Laws of Logarithms to expand the expression.
ln
52.
x8
x!9
5x + 9
0/1 points
SPreCalc6 4.4.048.MI. [1615123]
-
SPreCalc6 4.4.050.MI. [1615134]
-
Use the Laws of Logarithms to combine the expression.
log4(x2 ! 36) ! log4(x ! 6)
53.
0/1 points
Use the Laws of Logarithms to combine the expression.
ln(a + b) + ln(a ! b) ! 8 ln c
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54.
11/26/11 3:27 PM
0/1 points
SPreCalc6 4.4.053. [1614330]
-
SPreCalc6 4.4.052. [1616083]
-
SPreCalc6 4.5.008. [1616178]
-
Use the Laws of Logarithms to combine the expression.
1 log(x + 2)4 + 1 log x6 ! log(x2 ! x ! 6)3
4
3
55.
0/1 points
Use the Laws of Logarithms to combine the expression.
2(log6 x + 2 log6 y ! 4 log6 z)
56.
0/1 points
Find the solution of the exponential equation, correct to four decimal places.
55x ! 4 = 6
x=
1.0227
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57.
11/26/11 3:27 PM
0/1 points
SPreCalc6 4.5.009. [1615264]
-
SPreCalc6 4.5.010.MI. [1615240]
-
SPreCalc6 4.5.019. [1614493]
-
SPreCalc6 4.5.021.MI. [1613820]
-
Find the solution of the exponential equation, correct to four decimal places.
2ex = 10
x=
58.
1.6094
0/1 points
Find the solution of the exponential equation, correct to four decimal places.
3e13x = 11
x=
59.
0.0999
0/1 points
Find the solution of the exponential equation, correct to four decimal places.
e4x + 1 = 700
x=
60.
1.3878
0/1 points
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Find the solution of the exponential equation, correct to four decimal places.
5x = 4x + 8
x=
61.
49.7005
0/1 points
SPreCalc6 4.5.022.MI. [1616101]
-
SPreCalc6 4.5.029.MI. [1613765]
-
SPreCalc6 4.5.030.MI. [1613771]
-
Find the solution of the exponential equation, correct to four decimal places.
101 ! x = 9x
x=
62.
0.5117
0/2 points
Solve the equation. (Round your answers to four decimal places.)
e2x ! 8ex + 7 = 0
63.
x=
0 (smaller value)
x=
1.9459 (larger value)
0/1 points
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Solve the equation. (Round your answer to four decimal places.)
e2x ! ex ! 72 = 0
x=
64.
2.1972
0/1 points
SPreCalc6 4.5.037.MI. [1613809]
-
SPreCalc6 4.5.039. [1614887]
-
SPreCalc6 4.5.040.MI. [1614691]
-
Solve the logarithmic equation for x. (Round your answer to the nearest whole number.)
ln x = 5
x=
65.
148
0/1 points
Solve the logarithmic equation for x.
log x = !5
x=
66.
0.00001
0/1 points
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Solve the logarithmic equation for x.
log(x ! 3) = 2
x=
67.
103
0/1 points
SPreCalc6 4.5.043. [1613576]
-
SPreCalc6 4.5.042. [1615226]
-
SPreCalc6 4.5.045.MI. [1615581]
-
Solve the logarithmic equation for x.
3 ! log(5 ! x) = 2
x=
68.
-5
0/1 points
Solve the logarithmic equation for x.
log9(9 ! x) = 2
x=
69.
-72
0/1 points
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Solve the logarithmic equation for x.
log2 3 + log2 x = log2 5 + log2(x ! 2)
x=
70.
5
0/2 points
SPreCalc6 4.5.046.MI. [1615001]
-
SPreCalc6 4.5.049.MI. [1614967]
-
SPreCalc6 4.5.051. [1613549]
-
Solve the logarithmic equation for x.
2 log x = log 2 + log(3x ! 4)
71.
x=
2 (smaller value)
x=
4 (larger value)
0/1 points
Solve the logarithmic equation for x.
log3(x + 7) ! log3(x ! 7) = 3
x=
72.
98/13
0/1 points
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Solve the logarithmic equation for x.
log2 x + log2(x ! 7) = 3
x=
73.
8
0/1 points
SPreCalc6 4.5.053. [1615690]
-
SPreCalc6 4.5.055.MI. [1616162]
-
SPreCalc6 4.6.006. [1702503]
-
Solve the logarithmic equation for x.
log18(x ! 2) + log18(x + 1) = 1
x=
74.
5
0/1 points
For what value of x is the following true?
log(x + 3) = log x + log 3
x=
75.
3/2
0/3 points
This exercise uses the population growth model.
The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population
in 2000 was 11 million.
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in 2000 was 11 million.
(a) Find an exponential model n(t) = n0ert for the population (in millions) t years after 2000.
n(t) =
(b) Estimate the fish population in the year 2005. (Round your answer to three decimal places.)
11.622 million fish
(c) Sketch a graph of the fish population.
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76.
0/2 points
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SPreCalc6 4.6.007.MI. [1615355]
-
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The population of a country has a relative growth rate of 4% per year. The government is trying to reduce the growth rate to
3%. The population in 1995 was approximately 110 million. Find the projected population for the year 2035 for the following
conditions. (Round your answers to the nearest whole number.)
(a) The relative growth rate remains at 4% per year.
545 million people
(b) The relative growth rate is reduced to 3% per year.
365 million people
77.
0/3 points
SPreCalc6 4.6.013. [1613414]
-
A culture starts with 9000 bacteria. After one hour the count is 10,000.
(a) Find a function that models the number of bacteria n(t) after t hours. (Round rate r to three decimal places.)
n(t) =
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
11,100 bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
6.6 hr
78.
0/5 points
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SPreCalc6 4.6.014.MI. [1613463]
-
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The count in a culture of bacteria was 600 after 2 hours and 38,400 after 6 hours.
(a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your
answer to the nearest whole number.)
104 %
(b) What was the initial size of the culture? (Round your answer to the nearest whole number.)
75 bacteria
(c) Find a function that models the number of bacteria n(t) after t hours. (Round rate r to two decimal places.)
n(t) =
(d) Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.)
8,100 bacteria
(e) When will the number of bacteria be 75,000? (Round your answer to two decimal places.)
6.64 hr
79.
0/3 points
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SPreCalc6 4.6.015.MI. [1702520]
-
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This exercise uses the population growth model.
The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows
exponentially.
(a) Find a function that models the population (in millions) t years after 1990. (Round your r value to six decimal
places.)
n(t) =
(b) Find the time required after 1990 for the population to double. (Round your answer to one decimal place.)
53.6 yr
(c) Use the function from part (a) to predict the population of California in the year 2008. (Round your answer to two
decimal places.)
37.56 million
80.
0/1 points
SPreCalc6 4.6.019. [1614298]
-
This exercise uses the radioactive decay model.
The half-life of strontium-90 is 28 years. How long will it take a 80-mg sample to decay to a mass of 32 mg? (Round your
answer to the nearest whole number.)
37 yr
Assignment Details
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Name (AID): Review problems for Test 4 (Sec 7.4 to 4.6) (2159091)
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Category: Test
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