Stewart J. College Algebra: Concepts and Contexts
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A4 Answers to Selected Exercises and Chapter Tests
0
40
50
30
20
10
123 564
x
y
(iii) 2. constant; ; yes 3. 48
4.
7. (a)
(b) (4, 33), (5, 40), (6, 47)
(c)
y = 5 + 7x
C = 110 + 49x
- 6P = 15h
9. (a)
(b) (4, 43), (5, 40), (6, 37)
(c)
B = 55 - 3A
0
50
55
45
40
35
123 54
B
A
11. (a) 13, 13, 13 (b) Yes; (c) (4, 257),
(5, 270), (6, 283) 13. (a) , , (b) No (c) Not
linear 15. 17.
19. (a)
(b)
C = 19 + 10h
y = 1000 - 1000xy = 10 + 5x
- 5- 3- 4
y = 205 + 13x
(c) $69.00
21. (b) (c) 177.188°F 23. (b)
(c) 3825 lb 25. (a) (b) $250,000
Algebra Checkpoint 1.4
■
page 44
1. 3 2. 3. 10 4. 5. 14; 6. 2 or ; 3
7. 3; no solution 8. 3 or ; 9. 10.
11. 12. 13. 14.
15. 16. 17.
18.
1.4 Exercises
■
page 44
1. (a) output (b) x, y 2. (a) y, one (b) x, y
3. 4. (a) Vertical Line Test (b) (i)
5. (a) False (b) True (c) False (d) True
7. Yes 9. No 11. (a) No (b) Yes; y independent,
x dependent 13. (a) Yes; x independent, y dependent
(b) No 15. (b) (c) 17. (b) 1 (c) - 2- 3- 1
18 - 2 = 16
R = ; 31p
y = ; 31xh =
2
w - 3
t =
3s
4 + s
p = 4rt =
2
3x
y = 21
3
xz =
r
3
T =
P
6
x =
y - 5
3
4
3
- 3
- 2- 1
14
3
-
1
2
S = 150 + 10y
P =
17
20
MB = 212 - 1.8E
0
20
10
40
50
30
0.5 1 1.5 2.5 32
C
h
19. (a) x independent, y dependent (b) 14
21. (a) l independent, w dependent (b) 44 23. (a) Yes
(b) Yes 25. (a) No (b) Ye s 27. (a) Yes (b) Yes
29. Yes; 31. No 33. Ye s 35. No 37. Yes 39. Yes
41. No
43. (a)
- 2
1
0
2
y
x
0
2
2
y
x
(b) Yes; y ⫽ 2x
2
45. (a)
2
0
1
y
x
(b) Yes; y =
B
3
x
3
49. (a) y = 3x + 2
(b) No
47. (a)
1
0
4
y
x
(b) (c)
x y
-2
-1
0
1
2
-4
-1
2
5
8
51. (a)
(b) (c)
x T
0
10.00
20.00
30.00
40.00
0
0.80
1.60
2.40
3.20
T = 0.08x
0
3.0
2.0
2.5
1.5
1.0
0.5
10 20 30 40
T
x
Answers to Section 1.6 A5
53. (b) 0; 22 (c) $85,000 55. The cost of a load of hay is
$15 plus $25 per bale.
C = 15 + 25x
0
15
1
C
x
x C
0
1
2
3
4
5
15
40
65
90
115
140
57. (b) $1500 (c) (d) 334 tickets (x is
333.3, but you can’t buy just one-third of a ticket!)
59. (a) (b) 6 cm/s; 5.76 cm/s; 0 cm/s
(c) /s; /s- 5.76 cm- 0.24 cm
√ ⫽ 2410.25 ⫺ r
2
2
x =
P + 5000
15
61. (a) (b) No
0
30
35
40
45
50
60
65
55
45 55 65 75
y
x
63. (a)
H 60 62 63 65 65 68 70 71 75 75
y 27 29 31 22 31 25 27 27 24 30
(b) (65, 22), (65, 31)
(c) No
65. (a) Yes (c) Because there can be only one measurement
at any given time.
1.5 Exercises
■
page 58
1. x, y, value 2. 5, 1 3.
4. domain, range 5. (a) f, g (b) 10, 0 6. (2, 7), (4, 3),
(6, 7) 7. The difference between 5 squared minus 2 and
squared minus 2 8. (a) False (b) False 9. (a) f (b) x,
(c) “Multiply by 2, then add 1.” (d) 21; 21 is the
value of the function at 10. 11. (a) h (b)
(c) “Subtract two, then square the difference.” (d) 64; 64 is
the value of the function at 10. 13.
15. 17. “Divide by 2, then add 7.” 19. “Square,
multiply by 7, then subtract 5.” 21. “Add 3, cube the sum, then
multiply by 5.” 23. (a) Yes; (b) Yes;
25. (a) Yes; (b) Yes; 27. (a) Yes; y = 3x
2
x = 4y
3
y =
B
3
x
4
x =
y
5
y = 5x
y =
x
2
+ 7
4
y = 51x + 22
z, 1z ⫺ 2 2
2
2x + 1
- 2
f 1b 2- f 1a2; 5 - 1 = 4
(b) No 29. ; x independent, y dependent
31. ; w independent, y dependent 33. ;
r independent, S dependent 35. (a) (⫺2, 1), (⫺1, ⫺5),
(0, ⫺7), (1, ⫺5), (2, 1) (b) 8 37. (a) (⫺3, ⫺2), (⫺1, 6),
(0, 25), (1, 62), (2, 123) (b) 98 39. (a) 0 (b)
(c) 0 (d) 41. (a) (b) 3 (c)
(d) 43. (a) ;
(b) The surface area of spheres with radii of 2 and 3,
respectively (c) 45.
47. 49. 51.
53. 55. (a) 1 (b) 0 (c) 2 (d) 1 57. (a) 9
(b) 0 (c) 4 (d) 2 59. (a) 4 (b) (c) 0
(d) 0
61. (a) 28.14 mi; the maximum distance you can see from a
height of 0.1 mi (b) 41.26 mi (c) 235.6 mi (d) 29.01 mi
63. (a) 11,400 ft, 6600 ft; the skydiver’s height above the
ground after 10 s and 20 s, respectively (b) Yes, she was
3784 ft above the ground (c)
65. (a) 7.66 billion dollars, 9.49 billion dollars; the box office
revenue in 2000 and 2006, respectively (b) 2003, 2006
(c) 1.83 billion dollars 67. (a) $0, $960, $2350; the tax on
incomes of $5000, $12,000, and $25,000, respectively
(b) $1600 (c) $176,000 69. (a) , x (b) $90, $100,
$105; the cost of an order of $75, $100, or $105 worth of books.
71. (a) , 0, (b) $150, $0, $150
(c) 25 mi/h or 80 mi/h
151x - 65215140 - x2
x + 15
- 10,000 ft
- 1
5x
冨 x 7 46
5x
冨 x Ú 565x 冨 x ⫽ 365x 冨 - 1 … x … 56
5x
冨 - q 6 x 6 q660p L 188.50
36p L 113.1016p L 50.2712c - 1
1513a
2
+ 2a
2 + 212
S = 4pr
2
y = 3w
2
- 1
y = 3x
2
- 1
Algebra Checkpoint 1.6
■
page 70
1. (iii) 2. (iii) 3. (iii) 4. (iv)
5. (a) (b)
0
200
_2
2
_5
2
_2
2
_8
2
_3
3
_1
3
_2
3
(c) (d)
1.6 Exercises
■
page 71
1. , , 10, 10 2. 3 3. 5 4. (a) IV (b) II (c) Ix
3
+ 2f 1x2
(d) III 6. The calculator interprets as or
; the calculator interprets as or
.y = 5
y =
x
x
+ 4y = x>x + 4y =
1
3
x
y =
x
1
3
y = x^1>3
A6 Answers to Selected Exercises and Chapter Tests
x
f 1x 2
-3
-2
-1
0
1
2
3
5
5
5
5
5
5
5
1
0
1
y
x
7.
x
h 1x 2
-3
-2
-1
0
1
2
3
15
5
-1
-3
-1
5
15
x
F1x 2
-4
-2
0
2
4
8
0
2
213
212
16
12
9.
y
5
0x
2
11.
2
0
1
y
x
13. 15.
17. 19.
1
0
2
y
x
y
2
0x
1
21. 23.
y
x
2
0
2
_2
_2
y
2
_5
0
x
5_5
5
_5
_5
5
x
y
y
0x
4_4
_4
4
25. 27.
29. 31.
x
y
1
0
1
y
0x
5
5
_5
_2
x
f
g
h
y
1
0
2
y
0x
h
f
g
1
1
33. 35.
y
1
0x
g
f
h
1
_10
20
_4
10
37. 39.
_50
100
_4
6
_1
8
_20
2
Answers to Section 1.7 A7
41. Yes, two
43. 45.
y
0
x
5
2
_5
_2
y
0x
5
7
_5
0
0.020
0.015
0.010
0.005
567 9108
T
r
47. 49.
5_50
_5
5
x
y
0
Level
Time
51.
J F M A M J J A S O N D
Month
Sales
53.
r T(r)
5 0.02000
6 0.01389
7 0.01020
8 0.00781
9 0.00617
10 0.00500
0
5
7
5
P
x
55. (a) (b) The change in toll at
the times that morning and
afternoon rush hour start
and stop
Algebra Checkpoint 1.7
■
page 81
1. (a) The set of values greater than or equal to 1 and less than
or equal to 4 (b) [1, 4]
(c)
41
2_3
_3_10
2. (a) The set of values greater than or equal to and less
than 2 (b)
(c)
3- 3, 22
- 3
3. (a) The set of values greater than and less than
(b)
(c)
1- 10, - 32
- 3- 10
0
4. (a) The set of values greater than or equal to 0 (b)
(c)
30, q 2
62
5. (a) The set of values greater than 2 and less than 6
(b)
(c)
5x
冨 2 6 x 6 66
6. (a) The set of values greater than and less than or equal
to 3 (b)
(c)
5x
冨- 4 6 x … 36
- 4
3_4
2
_1
7. (a) The set of values less than 2 (b)
(c)
5x 冨 - q 6 x 6 26
8. (a) The set of values greater than or equal to
(b)
(c)
5x
冨 - 1 … x 6 q6
- 1
9. (a) The set of values greater than 1 and less than 5
(b) (c) (1, 5) 10. (a) The set of values
greater than or equal to and less than 1
(b) (c) 11. (a) The set of values
less than or equal to (b)
(c) 12. (a) The set of values greater than or equal
to and less than or equal to 0 (b)
(c)
1.7 Exercises
■
page 82
1. a, 4 2. x, y, [1, 6], [1, 7] 3. (a) increase, [1, 2], [4, 5]
(b) decrease, [2, 4], [5, 6] 4. (a) largest, 7 or 6, 2 or 5
(b) smallest, 2, 4 7. (a) (b) Domain: ;
range: (c) (d) (e) 2
9. (a) 3, 2, ⫺2, 1, 0 (b) Domain: ; range:
11. (a) (b) ; (c)
13. (a) (b) ,
(c) 1- 0.46, 1.462
31.46, q 21- q, - 0.464- 0.46, 1.46
1- 1, 3233, q 21- q, - 14- 1, 3
3- 2, 343- 4, 44
3- 3, 24- 3, 2, 43- 1, 44
3- 3, 441, - 1, 3, 4
3- 3, 04
5x
冨 - 3 … x … 06- 3
1- q, - 24
5x
冨 - q 6 x …-26- 2
3- 1, 125x
冨 - 1 … x 6 16
- 1
5x 冨 1 6 x 6 56
A8 Answers to Selected Exercises and Chapter Tests
_3
3
_3
3
_4
2
_4
4
(b) Domain: ; (b) Domain: ;
range: range:
19. (a) 21. (a)
1- q, 0 41- q, q 2
1- q, q 21- q, q 2
(b) Domain: ; (b) Domain: ;
range: range:
23. (a) and [2, 4] (b) [1, 2] 25. (a) and
[1, 2] (b) , , [2, 3]
27. (a) 29. (a)
3- 1, 143- 3, - 24
3- 2, - 143- 1, 14
30, q 230, 4 4
31, q 23- 4, 44
_0.8
4.8
_4.75
(b) Increasing: ; (b) Increasing:
decreasing: and ; decreasing:
31. (a)
3- 1, 24
32, q 21- q, 2.5 4
1- q, - 1432.5, q 2
_1
3
_1
9
10
_10
7_2
(b) Increasing: and ; decreasing:
33. (a) Local maximum 2 when ; local
minimum when , local minimum 0 when
(b) Increasing: and ; decreasing: and
[0, 2] 35. (a) Local maximum 0 when , local maximum
1 when ; local minimum when , local
minimum when (b) Increasing: and [1, 3];
decreasing: , [0, 1] and 37. (a) Local
maximum 0.38 when ; local minimum when
(b) Increasing: and ;30.58, q 21- q, - 0.584x = 0.58
- 0.38x =-0.58
33, q 21- q, - 24
3- 2, 04x = 1- 1
x =-2- 2x = 3
x = 0
1- q, - 2432, q 23- 2, 04
x = 2x =-2- 1
x = 03- 1.55, 0.224
30.22, q 21- q, - 1.554
20
_25
5_3
decreasing: 39. (a) Local maximum 5.66 when
(b) Increasing: ; decreasing: [4, 6]
41. (a) 500 MW, 720 MW (b) Just before noon
(c) Between 3:00
A.M. and 4:00 A.M. (d) About 375 MW
43. (a) 32°F, 20°F (b) T(19) (c) Day 2, days 6–10, days
12–25, day 15 (d) 7°F 45. (a) Increasing: [0, 30] and
[32, 66]; decreasing: [30, 32] (b) The person lost a lot of
weight in a short period of time, then gained it back within
2 years. 47. (a) Yes; runner B (b) 10 s after start (c) [0, 10]
49. (a)
1- q, 4 4x = 4
3- 0.58, 0.584
3
_3
5_5
(b) Increasing ; decreasing [5.1, 7.5] (c) 4600; E is
minimized when the velocity is 7.5 mi/h 51. (a) Maximum
concentration is at 0.3 h (b) Increasing: [0, 0.3]
(c) Decreasing: [0.3, 3]
1.8 Exercises
■
page 96
1. 3. 5.
7. 9. 11.
13. (b) (c) Maximum product occurs
when both numbers are 9.5. 15. (b)
(c) The maximum product occurs when both values are .
17. (a) (b) $2300
19. (a) (b) $53.33 (c) 2343.75 mi
21. (a)
C 1x 2=
32
300
x
C 1x 2= 200 + 3.5x
- 12
f 1x 2=-x1x + 242
f 1x 2= x119 - x2
A 1h 2= h
2
V1x 2= x
3
A 1x 2= x
2
+ 4x
P 1x 2= 2x
2
S 1n 2= 2n + 1N 1w2= 7w
37.5, q 2
13,000
4000
10
5.1
Number
of guests
Hall DJ Caterer Cake Total
10 $700 $300 $185 $15 $1200
20 $700 $300 $370 $30 $1400
30 $700 $300 $555 $45 $1600
40 $700 $300 $740 $60 $1800
50 $700 $300 $925 $75 $2000
(b) (c) $2500 (d) 200 people
23. (a)
C 1x 2= 1000 + 20x
Number
of frames
Number
that are $10
Number
that are 1¢
Total cost
2 1 1 $10.01
4 2 2 $20.02
6 3 3 $30.03
8 4 4 $40.04
10 5 5 $50.05
15. (a) 17. (a)
(b) (c) $100.10C 1x 2= 5.005x
0
2
1
y
x
Answers to Chapter 1 Review A9
25. (a)
Width
(in.)
Height
(in.)
Depth
(in.)
Volume
(in
3
)
3 7 3 63
4 8 3 96
5 9 3 135
6 10 3 180
7 11 3 231
(b) (c) (d) 8.20 in.420 in
3
V1x 2= 3x14 + x 2
550
12
0
27. (a) (b) (c) 5.94 in.1500 in
3
V1x 2=
3
2
x
3
550
7
0
(d)
29. (b) (c) 600 ft by 1200 ft
31. (a) (b) [1.17, 3.90]
(c)
1.9 Exercises
■
page 108
1. ; 2.
3. 5. 7.
9. 11. 13.
15. 17. 19.
21. (a) (b) 13,571 lb (c) 5182 lb
23. (a) (b) $3600 25. (a)
(b) 5 m 27. 29. 508.5 Hz4.4 ⍀
x =
hy
6 - h
P = n1p
s
- p
o
2
A = 19
˛
n
G
L = 2pr + 2xA = wl + 2wh + 2lht =
d
r
P = 2mnS = m
2
+ n
2
A =
a
1
+
a
2
2
w =
S - 2lh
21l + h2
R
1
=
RR
2
R
2
- R
R =
PV
nT
t =
d
r
; t =
350
55
L 6.4 h2 * 20 = 408 * 12 = 96
262.7 in
3
V1x 2⫽ x112 ⫺ 2x 2120 ⫺ 2x2
A 1x 2= x12400 - 2x2
36.7, q 2
31. (a) 49,900k, 4,000,000k; the second rate is larger.
(b) 0; there is no one left to infect.
33. (a)
(b)
√ =
B
94,700w
S
0
12
15
9
6
3
246 10128
y
x
Bird w/S V (mi/h)
Common tern 0.00342 18.00
Black-headed gull 0.00433 20.26
Common gull 0.00456 20.77
Royal tern 0.00647 24.75
Herring gull 0.00750 26.65
Great skua 0.00909 29.34
Sooty albatross 0.01189 33.55
Wandering albatross 0.02042 43.97
(c) 47.45 mi/h
Chapter 1 Review Exercises
■
page 115
1. (a) (b) 4 3. (a) {(2, 14), (4, 12), (6, 12), (8, 8),
(10, 5), (12, 3)} (b) Domain: {2, 4, 6, 8, 10, 12}; range:
{3, 5, 8, 12, 14} (c) 12
(d) (e) Yes; the y values get
smaller as the x values get
larger.
4
1
3
5. (b) 20 (c) 4, 8 (d) Maximum: 22; minimum: 6.
7. (a) (b) 13; 66 9. (a)
(b) 9.5; 11. (a) Yes (b) (c) 1.5, ,
13. Yes 15. (a) No (b) Yes; y independent,
x dependent 17. (a) x independent, y dependent (b) 28
(c) 24 19. (a) x-intercepts: ; y-intercept: 0 (b) Ye s
(c) ; 12 21. (a) No (b) Yes 23. (a) Ye s
(b) Yes
25. (a)
(b) (c)
(d) f 1x2= 2x - 7
x y
0
1
2
3
4
-7
-5
-3
-1
1
y = 2x - 7
y = x
3
- 4x
- 2, 0, 2
- 3.1
- 0.810.7 ⫺ 2.3x- 70
y = 20 - 3xy = 6 + 2x
y
0x
2
5
A10 Answers to Selected Exercises and Chapter Tests
27. (a)
(b) (c)
(d)
29. (a) Divide by 3, then add 5.
(b) ; x independent, y dependent (c)
31. (a) Subtract three, square, then multiply by .
(b) ; x independent, y dependent (c) 2
33. (a) 3 (b) 3 (c) 9 (d) 35. (a) 2
(b) 0 (c) 3 (d) 300
37. {(⫺2, 9), (⫺1, 7), (0, 5), (1, 3), (2, 1), (3, ⫺1), (4, ⫺3)}
2a
2
- 4a + 3
y =
1
2
1x - 32
2
1
2
2
3
y =
x
3
+ 5
f 1x 2=
1x + 22
2
3
x y
-5
-2
1
4
7
3
0
3
12
27
y =
1x + 22
2
3
y
0x
1
2
39. 41.
y
x
0
1
1
43. 45.
y
x
1
0
1
47. 49.
y
x
1
0
1
_7
11
_2
6
_1
3
_2
6
y
0x
1
1
51. (a) (b) 3 (c) 0, 2 (d) Domain: ;
range: (e) Increasing: ; decreasing:
and [1, 2]
53. (a) 55. (a)
3- 2, - 143- 1, 143- 1, 24
3- 2, 24- 1, 1, 1
_1
4
_2
2
(b) Domain: ; (b) Maximum 1 at ;
range: [0, 3] minimum at
(c) Increasing: ;
decreasing: 30,
3
2
4
3-
3
2
, 04
x = 2- 3
x = 03-
3
2
,
3
2
4
_
4
7
_1
3.5
lb
0
y
r
100
200
300
50
150
250
350
2010 40 5030
0
100
200
300
50
150
250
350
2010 40 5030
lb
yr
(f) All except Andrea have
weights that are more than
five times their age.
57. 59.
61. 63. (a) Average 26 years, median 18 years
(b) Average 153 lb, median 131 lb; John brings the average up.
The median is a better description. (c) {(10, 90), (16, 114),
(16, 142), (20, 120), (46, 310), (48, 142)}; domain: {10, 16,
20, 46, 48}, range: {90, 114, 120, 142, 310}
(d) No (e) Generally, as the age
increases the weight
increases.
√ =
B
2k
m
S = 2n
1
+ 2n
2
+ 2n
3
H1d 2= 24d
Length
(in.)
Width
(in.)
Height
(in.)
Volume
(in
3
)
36 14 10 5040
40 12 10 4800
36 12 12 5184
36 16 8 4608
72 3 3 648
44 10 10 4400
Answers to Chapter 1 Test A11
65. (a) 6 (b) 6 (c) 6.5, 6 67. (a) Average: 2.5; median: 2
(b) Average: 14 lb; median: 14.5 lb (c) Jack 4.5 lb, Helen
4.0 lb, Steve 5.5 lb, Kalpana 5.5 lb, Dieter 6.5 lb, Magda 8 lb
(d) Magda (e) 5.6 lb
69. (a) 75, 108, 132, 135, 100, 75
(b) (c) The profit increases
until the price is $1.00;
then it decreases. The best
price seems to be $1.00.
0
50
140
130
120
110
100
90
80
70
60
0.80.4 1.210.60.2 1.4
Price
Profit
0
120
160
200
240
280
120 160 200 240 280
y
x
0
2000
1500
1000
500
2000 4000 6000 10000 12000 140008000
y
x
71. (a) (b) No
73. (a) 0, 400, 3000
(b)
(c) $8000, $13,333.33 (d) $1200
75. (a) Domain: [0, 365]; range: [25, 87] (b) Increasing:
[0, 150] and [300, 365]; decreasing: [150, 300] (c) 75 ft
(d) 87 ft on day 150 77. (a)
(b) Width along road 30 ft; length 40 ft (c) 15 ft to 60 ft
79. (a) 5 in.
(b)
C1x 2= 8x +
7200
x
0
4
6
8
2
_2
_4
_6
123 564
y
x
Chapter 1 Test
■
page 126
1. (a) 4.5, 5 (b) 0.4, 1.2 2. (a) {(0, 1), (1, 5), (2, 7), (3, 7),
(4, 5), (5, 1), (6, ⫺5)} (b) Domain: {0, 1, 2, 3, 4, 5, 6}; range:
{⫺5, 1, 5, 7}
(c) (d) Yes (e) Yes; y increases,
then decreases as x increases.
(f) 1, 4
y
0x
2
2
3. (a) (b) 6.25, 9.00
(c)
y = 4 + 0.5x
0
200
400
600
800
1000
1200
50 100 150 200 250
C
x
4. (a) No (b) Ye s 5. f 1x2=
x
2
- 4
5
12,000
60
0
8. (a) (b) 10,000 ft at 25 s
(c) At
(d) [25, 50]; falling to the
ground
t = 50 s
9. (a) (b) h =
A - 2lw
2l + 2w
1056 cm
2
6. (a)
(b) 15,200, 17,000, 33,000, 32,000 (c) 39,000, 42,000
7. (a)
(b) (c) $500, $1100; the cost
with 50 guests and with 200
guests (d) 75 guests
C = 300 + 4x
f1x 2= •
0.80x if x 6 20,000
x - 5000 if 20,000 … x 6 40,000
x - 8000 if x Ú 40,000
A12 Answers to Selected Exercises and Chapter Tests
13. 3 15. 17. 3 19.
21. (a) (b) (i) 3284 (ii) 1709
(iii) 8300 (c) 1950 to
1960
- 2- 2
y
0
x
100
80
60
40
20
108642
y
0
x
75
55
65
45
35
25
15
201612
A
g
e
84
Height
Chapter 2
2.1 Exercises
■
page 148
1. (a) (b) 2. , h, f
3. (a) True (b) True 4. f, 5. f : constant.; : increasing;
h: decreasing 7. 9.
11. (a) (i) 20 (ii)
(b) (c) and ; 30x = 2x = 1
- 6
-
4
5
2
3
gg
g
10 - 3
5 - 2
=
7
3
change in y
change in x
=
f 1b 2- f 1a2
b - a
y
0
x
500,000
400,000
300,000
200,000
100,000
15012090
Years since 1850
6030
Population
23. (a) 19.25 in., 39.63 in., 49.25 in. (b) 5.1 in./year,
2.4 in./year; the first four years
(c)
Between his 15th and 16th
birthdays
y
x
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Year
1999
Value (U.S. dollars)
2000 2001 2002 2003 2004 2005 2006 2007 2008
(b) (i) 0.0667 per yr (ii) 0.0725 per yr (iii) 0.0367 per yr
(c) From 2003 to 2004 27. (a) Skater B (b) A: 20 m/s, B:
10 m/s (c) A: 6.67 m/s, B: 20 m/s 29. (a) 160 ft/s
(b) 480 ft/s 31. (a) /s (b) /s (c) /s
(Negative speeds because height is decreasing.)
2.2 Exercises
■
page 161
1. (a) linear (b) (c) line
2. (a) ; 7 (b) line; , 7
3. y; x; 4. ; 5; 5 5.
6. Positive: upward; negative: downward 7. Yes; slope: 0,
y-intercept: 2 8. (a) Increases the steepness of the line
(b) Increases the y-intercept 9. Yes 11. No
13. Yes 15. Yes
17. 19.
g- 5
5 - 1
2 - 0
= 2
- 2- 2
f 1x 2= b + mx
- 84 ft- 48 ft- 32 ft
1
0
5
y
x
1
0
2
y
x
21. (a) 2 (b) 2 (c) 2
23. (a) (b) (c)
25. (a) 27. (a)
- 2- 2- 2
1
0
2
y
x
1
0
1
y
x
(b) 2 (c) 2 (b) (c)
29. (a) 31. (a)
- 1- 1
(b) 3 (c) 3 (b) 2 (c) 2
1
0
2
y
t
1
0
2
y
t
25. (a)
Answers to Section 2.3 A13
33. (a)
(b) (c)
35. 37. 39. (a) ; 3
(b) 41. (a) , 12 (b)
43. 45. 47. 49. (a) 1, 3 (b)
51. (a) , 2 (b) 53. (a) Yes
(b) 32,400 thousand tons (c) 4 thousand tons per day
(d)
y = 2 -
1
2
x-
1
2
y = 3 + x-
1
2
1
6
1
2
f 1x 2= 12 - 2x- 2f 1x 2= 3 +
1
2
x
1
2
h1x 2= 9 - 3xf 1x 2=-3 + 7x
- 0.5- 0.5
1
0
1
y
x
y
0
x
32,450
32,500
32,550
32,600
5040302010
55. 57. Brianna: , or ; Meilin:
, or 59. (a) Jari (b) Jari: 70 mi/h;
Jade: 60 mi/h (c) Jari: ; Jade:
2.3 Exercises
■
page 173
1. ; 2. ;
3. (a) zero; (b) undefined;
4. point-slope; 2; or
5. (a) horizontal; zero (b) vertical; undefined (c)
6. line; 5; 3 7. The temperature is increasing; decreasing;
remaining the same. 8. No 10. and
; , yes 11.
13. 15. 17.
19. 21. 23. (a)
(b)
(c)
y = 4 + 2x
y - 4 = 21x - 02y =
5
2
-
5
4
xy =-
4
3
+ 3x
y = 6 - 3xy = 5 +
1
2
xy =-3 - x
y = 2 + 5xy = 3x - 1y - 5 = 31x - 22
y - 2 = 31x - 12
y = 2
y - 7 = 21x - 32y - 5 = 21x - 22
x = 2y = 3y - 2 = 31x - 12
y - y
1
= m1x - x
1
2y = 4 + 2xy = b + mx
d1t 2= 10 + td1t 2=
7
6
t
- 8%- 0.08
- 5%- 0.05V1t2= 2 + 0.5t
1
0
2
y
x
25. (a)
(b)
(c)
y =
19
3
+
2
3
x
y - 7 =
2
3
1x - 12 27. (a)
(b)
(c)
y = 2 -
1
3
x
y - 4 =-
1
3
1x + 62
29. (a)
(b)
(c)
y =-5
y + 5 = 01x - 42
1
0
2
y
x
31. (a)
or
(b)
(c)
y = 3 + x
y - 7 = 11x - 42
y - 1 = 11x + 22
3
0
4
y
x
33. (a)
or
(b)
(c)
y = 4 - 3x
y + 2 =-31x - 2 2
y - 7 =-31x + 1 2
35. (a)
or
(b)
(c)
y =
1
3
+
4
3
x
y - 7 =
4
3
1x - 52
y - 3 =
4
3
1x - 22
2
0
2
y
x
1
0
1
y
x
1
0
2
y
x
1
0
1
y
x
1
0
1
x
y
37. 39. 41. 43.
45. 47. 49. , 51. ,
53. (a) (b) 5, 3
(c)
-
3
5
b = 3
m =
6
5
b = 6m =-
3
4
x = 8x = 8
y = 10y =-7y =-3 +
3
2
xy = 4 - x