Solve the problem.
106)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) =1500
x + 50 , what do
400 units cost?
106)
A)
$1499.88
B)
$12,000.00
C)
$139.99
D)
$1333.33
Solve the equation. Round decimal answers to the nearest thousandth.
107)
9e9x+8=2
107)
A)
0.604
B)
–2.382
C)
–2.716
D)
–1.056
Use natural logarithms to evaluate the logarithm to the nearest thousandth.
108)
log 3238.0
108)
A)
9.962
B)
0.100
C)
4.981
D)
0.239
Classify the function as even, odd, or neither.
109)
f(x) = – 4x3
109)
A)
Even
B)
Odd
C)
Neither
Solve the problem.
110)
How long will it take for prices in the economy to double at a 7% annual inflation rate? Round to
the nearest hundredth when necessary.
110)
A)
9.01 yr
B)
23.45 yr
C)
10.24 yr
D)
16.24 yr
111)
Use the formula P = Iekt. A bacterial culture has an initial population of 10,000. If its population
declines to 3000 in 8 hours, what will it be at the end of 10 hours?
111)
A)
3500 bacteria
B)
1110 bacteria
C)
2220 bacteria
D)
403 bacteria
Evaluate the function.
112)
f(x) =2x
3x + 10 ; Find f(–2).
112)
A)
–2
5
B)
2
13
C)
– 1
D)
2
3
B)
Write the expression using base e rather than base 10.
113)
10x +8
113)
A)
e10(x +8)
B)
e(ln 10)(x +8)
C)
(x +8)e10
D)
10ex +8
B)
Determine whether the rule defines y as a function of x.
114)
y =x2+4
114)
A)
Function
B)
Not a function
B)
Graph the parabola and give its vertex, axis, x–intercepts, and y–intercepts.
115)
f(x) =x2+ 2x – 3
115)
62
B)
A)
vertex (1, –4); axis is x =1;
x–intercepts are –1 and 3; y–intercept is –3
B)
vertex (1, 4); axis is x =1;
x–intercepts are –1 and 3; y–intercept is 3
C)
vertex (–1, –4); axis is x = – 1;
x–intercepts are 1 and – 3; y–intercept is –3
63
D)
vertex (–1, 4); axis is x = – 1;
x–intercepts are 1 and – 3; y–intercept is 3
Solve the problem.
116)
A certain noise has intensity 4.75 ×108I0. What is the decibel rating of this sound? Use the formula
D = 10 log I0, where I0 is a faint threshold sound, and I is the intensity of the sound.”
116)
A)
9 decibels
B)
77 decibels
C)
200 decibels
D)
87 decibels
Solve the equation.
117)
5x=625
117)
A)
4
B)
3
C)
125
D)
5
Graph the indicated new function, given the graph for y = f(x).
64
118)
y = af(x), where a satisfies –1 < a < 0
118)
A)
B)
C)
D)
119)
y = af(x), where a satisfies 1 < a
119)
A)
B)
C)
D)
Solve the problem.
120)
In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t
and k is a growth constant equal to the percent of growth per unit time. How long will it take for
the population of a certain country to double if its annual growth rate is 2.1%? Round to the nearest
year.
120)
A)
14 yr
B)
95 yr
C)
33 yr
D)
1 yr
Solve the equation. Round decimal answers to the nearest thousandth.
121)
100.54x=20.17x
121)
A)
–2.765
B)
0.674
C)
–1.254
D)
0.000
Find the domain of the function.
122)
f(x) = log (x – 4)
122)
A)
x > 0
B)
x >4
C)
x > – 4
D)
x > 1
Solve the problem.
123)
Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by
y =312,500
x + 625 . What is the cost per ton for x =300?
123)
A)
$337.84
B)
$416.67
C)
$101,351.35
D)
$150,000.00
Find the domain of the function.
124)
f(x) = ln (3x – x2)
124)
A)
–3
x < 0
B)
x 3
C)
–3< x <3
D)
0 < x <3
Solve the problem.
125)
The amount of particulate matter left in solution during a filtering process decreases by the
equation P =400(2)–0.6n, where n is the number of filtering steps. Find the amounts left for n = 0
and n = 5. (Round to the nearest whole number.)
125)
A)
400, 3200
B)
800, 50
C)
400, 13
D)
400, 50
126)
The length and width of a rectangle have a sum of 180. What dimensions will give the maximum
area?
126)
A)
45 by 135
B)
90 by 90
C)
89 by 91
D)
45 by 45
Graph the function.
127)
y = – 2ex+ 5
127)
A)
B)
68
C)
D)
Solve the problem.
128)
Find the present value of the deposit. $2000 at 8% compounded monthly for 7 years. Round to the
nearest cent.
128)
A)
$3438.84
B)
$3494.84
C)
$1144.54
D)
$1200.54
Evaluate the function.
129)
f(x) = x2+ 3x – 5; Find f(0).
129)
A)
25
B)
0
C)
5
D)
–5
130)
f(x) =3x2+ 2x – 5; Find f(t – 1).
130)
A)
3t2– 13t + 0
B)
3t2– 4t + 0
C)
3t2– 4t – 4
D)
–4t2+ 3t – 4
69
Write the logarithmic equation in exponential form.
131)
log21
8= – 3
131)
A)
1
8
3
=2
B)
32=1
8
C)
28=3
D)
2–3=1
8
Solve the problem.
132)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) =300
x + 10 , what is the
unit cost for 10 units?
132)
A)
$15.00
B)
$30.00
C)
$20.00
D)
$3.00
Solve the equation. Round decimal answers to the nearest thousandth.
133)
e–0.04x=0.08
133)
A)
63.143
B)
–63.143
C)
–2
D)
2.526
70
Give the domain and range of the function.
134)
134)
A)
Domain (–, 0) ; Range (–, 0)
B)
Domain (–, ) ; Range [–6, )
C)
Domain (0, ) ; Range [15, )
D)
Domain (–, 0) (0, ) ; Range (–, 0) (0, )
Graph the parabola and give its vertex, axis, x–intercepts, and y–intercepts.
135)
f(x) = – x2– 6x – 8
135)
71
A)
vertex (–3, –1); axis is x = – 3;
x–intercepts are –2 and – 4; y–intercept is 8
B)
vertex (3, 1); axis is x =3;
x–intercepts are 2 and 4; y–intercept is –8
C)
vertex (–3, 1); axis is x = – 3;
x–intercepts are –2 and – 4; y–intercept is –8
72
D)
vertex (3, –1); axis is x =3;
x–intercepts are 2 and 4; y–intercept is 8
Use the graph to evaluate the function f(x) at the indicated value of x.
136)
Find f(1.5).
136)
A)
0.5
B)
–1
C)
–2
D)
None of these are correct.
Evaluate the logarithm without using a calculator.
137)
log7 1
343
137)
A)
3
B)
49
C)
–3
D)
–49
Graph the rational function.
138)
y =4
1–5x
138)
A)
B)
74
C)
D)
Write the logarithmic equation in exponential form.
139)
log 100 =2
139)
A)
1002= 10
B)
102=100
C)
10100 =2
D)
210 =100
Evaluate the function.
140)
f(x) =x – 7
x – 5 ; Find f(2).
140)
A)
5
3
B)
3
2
C)
–5
7
D)
7
5
Solve the problem.
141)
An investment of $13,335 earns 6% interest compounded monthly for 3 years. (a) What is the value
of the investment after 3 years? (b) If money can be deposited at 8% compounded quarterly, find
the present value of the investment. Round to the nearest cent.
141)
A)
(a) $14,157.47
(b) $12,834.21
B)
(a) $15,957.73
(b) $12,582.56
C)
(a) $16,957.73
(b) $14,892.16
D)
(a) $15,878.34
(b) $13,892.16
142)
A projectile is thrown upward so that its distance above the ground, in feet, after t seconds is
h = – 13t2+ 520t. What is its maximum height?
142)
A)
5200 ft
B)
3900 ft
C)
7800 ft
D)
2600 ft
Graph the rational function.
143)
y =x2+ 4x + 3
x +1
143)
A)
B)
76
C)
D)
Solve the problem.
144)
A function that might describe the entire Laffer curve is y = 0.5x(100 – x)(10000 –x2)where y is the
government revenue in hundreds of thousands of dollars from a tax of x percent, with the function
valid for 0
x
100. Find the revenue from a tax rate of 50%. Round your answer to the nearest
billion.
144)
A)
$938 billion
B)
$838 billion
C)
$963 billion
D)
$908 billion
Decide whether the graph represents a function.
145)
145)
A)
Function
B)
Not a function
Find f(x +
h) – f(x)
h.
146)
f(x) =8x2+ 6x – 3
146)
A)
8x + 6 + 16h
B)
16xh + 6h +6h2
C)
16x + 6
D)
16x + 6 + 8h
Write the logarithmic equation in exponential form.
147)
ln 1
e4= – 4
147)
A)
1
e4
e
= – 4
B)
e–4=1
e4
C)
1
e4
–4
= e
D)
–4e=1
e4
Give the domain and range of the function.
148)
148)
A)
Domain [–3, 9] ; Range [–8, 8]
B)
Domain [–8, 8] ; Range [–3, 9]
C)
Domain {–8, –4, –1, 1, 4, 8} ; Range {–3, 5, 9}
D)
Domain {–3, 5, 9} ; Range {–8, –4, –1, 1, 4, 8}
Solve the problem.
149)
A Community College wants to construct a rectangular parking lot on land bordered on one side
by a highway. It has 1200 feet of fencing to use along the other three sides. What should be the
dimensions of the lot if the enclosed area is to be a maximum? (Hint: Let x represent the width of
the lot, and let 1200 – 2x represent the length.)
149)
A)
400 ft by 800 ft
B)
300 ft by 900 ft
C)
300 ft by 600 ft
D)
400 ft by 400 ft
150)
How long will it take for prices in the economy to double at a 7% annual inflation rate? Round to
the nearest hundredth when necessary.
150)
A)
10.24 yr
B)
9.01 yr
C)
16.24 yr
D)
23.45 yr
Evaluate the logarithm without using a calculator.
151)
log6
4 1
36
151)
A)
1
2
B)
–2
C)
2
D)
–1
2
Use the properties of logarithms to find the value of the expression.
152)
Let logb6= a and logb5= c. Find logb36b4.
152)
A)
2b + a –4
B)
2ab
C)
2(a + b)
D)
2a +4