Stewart J. College Algebra: Concepts and Contexts
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17. Yes
19. (a)
(b)
(c)
y = 6 + 2x
y =
7
2
-
1
2
x
2
0
2
y
x
y=-x
7
2
1
2
y=1-
y=6+2x
x
1
2
21. (a)
(b)
(c)
y = 3 -
3
4
x
y = 3 +
4
3
x
2
0
2
y
x
y=3+ x
4
3
y=3- x
3
4
y=+ x
4
3
1
3
A14 Answers to Selected Exercises and Chapter Tests
55. (a) (b) ,
(c)
- 2
5
2
4
5
1
0
1
x
y
57. (a) (b) 4 mi/min or 240 mi/h
59. (a)
(b) (c) Slope: rate of
depreciation; y-intercept:
initial cost of computer
(d) $1150
V1t 2= 4,000 - 950t
y = 45 - 4x
61.
63. (a) y = 20 - 21x - 102= 40 - 2x
V1t 2= 4 + 0.5t
1234
0
1000
2000
3000
4000
y
t
510 2015
0
10
20
30
40
y
x
(b) 12; 28 (c) ; number of sales lost for each dollar
increase in the price (d) 40; the number of “sales” if the
feeders were free (e) 20; the price at which no feeders would
be sold
2.4 Exercises
■
page 184
1. slope; parallel 2. y-intercept; neither 3. (a) 3 (b) 3
(c) 4. (a) directly proportional; 3 (b)
5. (a) and have the greatest slope; and are parallel;
none are perpendicular. (b) has the greatest slope; and
are parallel; is perpendicular to and .
7. (a) True (b) False (c) True (d) False
8. w is directly proportional to x.
9. (a) They have the same (b) They have the same
slope. slope.
l
2
l
1
l
3
l
2
l
1
l
3
l
4
l
3
l
4
l
3
y = 3x-
1
3
- 2
_6
12
_3
3
b=0
b=1
b=2
b=3
_12
6
_3
3
b=0
b=_1
b=_2
b=_3
11. (a) They have the same x-intercept.
(b) They have the same x-intercept.
_5
5
_2
8
m=0
m=0.75
m=1.5
m=0.25
_5
5
_2
8
m=0
m=_0.75
m=_1.5
m=_0.25
13. (a)
(b)
y =-2 + 3x
15. (a)
(b)
y =
8
3
-
2
3
x
1
0
2
y
x
y=_4+3x
y=_2+3x
2
2
y
x
y=_2-
y= x-
2
3
2
3
8
3
x
23. (a) (b) (c)
25. (a) (b) (c)
27. (a) (b) (c) 29. 31.
33. 35. 37. 39.
41. 43. 45. 12 47.
49. y = 5376x
y = 5280xy = 7xT = kx
y = 6 + xy =
19
5
-
4
5
xy = 9 -
3
2
xx = 3
y = 2y = 6 + 4xl
1
l
2
l
3
y = 4 +
1
2
xy = 6 - 2xy = 4 - 2x
y =-6 -
1
3
xy =-9 + 3xy =-6 + 3x
Answers to Section 2.5 A15
53. (a) (b) 87,000 fl oz or 16.2 barrels
55. ; the interest rate 57. (a)
(b) (c) 32 N
2.5 Exercises
■
page 195
1. regression 2. (a) extrapolation (b) interpolation
3. Yes 4. (a) Regression line:
(b) Regression line:
5. (a)
y = 3.64x + 5.25
y = 4x + 6
k = 8
F = kxi = 0.06P
y = 0.000003x
0
5
10
15
20
30
25
7214365
y
x
(b) y =-1.98 + 5.0943x
7. (a)
0
16
17
18
19
21
22
20
8070 10090 120110
y
x
(b) y = 27.138 - 0.07743x
9. (a)
(b) y =-6.6245 + 0.8434x
11. (a)
(b) y = 1.719 + 2.0316x
0
5
10
15
20
25
1510 2520 3530
y
x
13. (a)
0
10
20
30
40
50
810624
Mauricio
Thanh
Distance from rapids
y
x
51. (a) Mauricio: ; Thanh:
(b) (c) No
y = 34 - 5xy = 45 - 5x
0
20
10
30
40
50
60
1052015 3025
y
x
(b) (c) 191.7 cmy = 82.65 + 1.8807x
0
155
150
160
165
170
180
175
4035 5045
Femur length (cm)
Height (cm)
55
y
x
15. (a)
0
5.5
5
6
6.5
7
8
7.5
4
8 12 16
Years since 1980
Ice extent (million km
2
)
20 24 28
y
x
(b) (c) 5.8 million km
2
y = 7.831 - 0.0689x
0
55
50
60
65
70
75
80
1920 1940 1960
Life expectancy (years)
1980 2000
y
x
17. (a)
(b) (c) The increase in life
expectancy per year
(d) 80.3 yr
y =-462.9 + 0.2708x
21. (a) Men’s: ;
Women’s:
(b)
y = 78.67 - 0.269x
y = 64.717 - 0.173x
y
x
10 20 30 80 9060 7040 50 100
Flow rate (%)
Mosquito positive rate (%)
15
20
5
10
25
0
19. (a) (b)
(c) The mosquito rate when
there is no flow
(d) 8.13%
y = 19.89 - 0.168x
y
x
20 40
Women
Men
60
Years since 1900
80 100
Record time (s)
50
60
70
80
0
x C(x) S(x)
6 7390 3450
12 8980 6900
18 10,570 10,350
24 12,160 13,800
30 13,750 17,250
36 15,340 20,700
A16 Answers to Selected Exercises and Chapter Tests
23. (a) (b)
(c)
y = 8988.2 + 561.4xy = 241.62 + 1316.7x
0
25,000
24,000
26,000
27,000
28,000
29,000
30,000
12 43
y
x
0
9500
9000
10,000
10,500
11,000
11,500
12 43
y
x
(d) 11,795 women in 2007
Algebra Checkpoint 2.6
■
page 206
1. (a) Yes; no (b) No; yes (c) No; yes 2. (a) 12
(b) 10 (c) 2 (d) (e) (f) 3. (a) 3
(b) (c) 3 (d) No solution (e) 4
2.6 Exercises
■
page 207
1. (a) two (b) one 2. (a) (b) 1
3. 4.
5. True 6. False 7.
9. 10 11. 10 13. 250 15. 30 17. 4 19. 2
21. 17.7 min 23. (a) About 24,650 days
(b) 24,650 days or 68 years 25. 168 chirps/min
27. (a) (b) $2800 at 4% andI = 0.04x + 0.045112,000 - x2
- 4y = 0.04x + 0.0511000 - x2
1000 - x; 0.04x; 0.0511000 - x2; 4000 = 500 + 10x
6 - 2 = 3x + 1
- 20
-
13
7
95
32
- 40
31. (a) Plan 1: ; plan 2: ;
(b) Plan 1; plan 2; 1100 miles 33. (a)
(b) (c) 1.55 hours; 111.6 miles
35. (a) $2.75 per bushel (b) $18.21 per bushel
(c) $5.88 per bushel; 13.1 billion bushels
Chapter 2 Review Exercises
■
page 222
1. 3. 5. 7 7. No
9. (a) 11. (a)
4
3
- 1
y = 65Ax +
1
6
B
y = 72x
C1x 2= 270C1x2= 105 + 0.15x
$9200 at 4.5% 29. (a) (b) 18 g
31. (a) (b) ,
33. 6.4 ft from the fulcrum
2.7 Exercises
■
page 215
1. (a) (b) ; 17,
(17, 41) 2. (a) equilibrium (b)
4. ; 5. (a) (2.5, 0.5) approximately
(b) ; (c) (2.4, 0.4) 7. (a) 2 (b) 2
9. (a) 2 (b) 2 11. 2 13. 3 15. 2 17.
19. (1, 3) 21. 23. ,
; , 25. Price: $21.81; amount: 13.82
27. (a) (b)
(c) 450 minutes
29. (a) (b)
(c) (d) 19 months
S1x 2= 575xC1x2= 5800 + 265x
g1x 2= 100f 1x 2= 10 + 0.20x
B
71
13
9
13
Ag1x2= 2 + 5x
f 1x 2= 5 +
2
3
x110, - 92
1- 3, - 12
y = 2 -
2
3
xy =-2 + x
y = 5 - 2ty = 2t
m
1
p + b
1
= m
2
p + b
2
3x - 102x + 7 =m
2
x + b
2
m
1
x + b
1
=
l = 9 cmw = 4 cmP = 2w + 21w + 52
G =
81
90 + x
(b) 2 (c) 2 (b) (c)
13. 15. 17.
19. 21. 23.
25. 27.
29. (a) Slope: ;
x-int: 2, y-int: 1
(b)
-
1
2
y = 26y = 4 -
4
3
x
y = 8 - 2xy = 9 - 6xy = 5x
f 1x 2= 4 -
1
2
xf 1x 2= 3 + 2xf 1x 2= 10 - 5x
-
1
2
-
1
2
2
0
1
y
x
(c) y = 1 -
1
2
x
1
0
2
y
x
1
0
1
y
x
31. (a) Slope: ; x-int: 4,
y-int:
(b)
- 3
3
4
(c)
(c) y =-5 -
5
4
x
y =-3 +
3
4
x
1
0
1
y
x
2
0
1
y
x
y=_2+
x-2y-8=0
2x+y-1=0
x
1
2
33. (a)
(b)
(c)
2x + y - 1 = 0
x - 2y - 8 = 0
35. 37. 39. 35 41. y = 25.4xy =-14 + 4xy =
1
2
x
Answers to Chapter 2 Test A17
0
4
2
6
8
10
12
14
16
21436587
y
x
45. (a)43. (a)
(b)
(c) Yes
y = 4.435 + 1.229x
(b), (c) (4, 12)
47. (a) 49. (a)
2
f
g
0
2
y
x
(b), (c) (b), (c)
51. (a)
A
9
5
,
48
5
B1- 1, 82
1
f
g
0
4
y
x
1
f
g
0
3
y
x
1
Regression line
0
1
y
x
(b) ; (c) ; (d)
(e) ; (f) (g) ;
(h)
53. (a)
y = 0.65 + 0.775x1- 4, - 172
- 5 + 3xy = 3 + 5x, y =
1
3
x =-1P
1
, P
2
y =
1
2
-
1
2
xy = 1P
1
, P
4
x =-1P
1
, P
2
100
50
0
150
200
250
300
1800
1840 1880 1920 1960 2000
y
x
(b) Increasing (c) 1.502 million per year (d) 0.709; 20.52
million per year (e) 1.38 million per year (f) 1990–2000;
3.27 million per year
55. (a) 1.4 inches per day (b)
(c) The slope is 1.4.
y = 14 + 1.4x
(d) 70 in. (e) 14 in. (f) 10 days (g) May 30
57. (a)
(b) (c) 38.4 ounces (d) 2036
y = 9.929 + 0.8143x
0
20
10
30
40
50
70
60
10 20 4030
y
x
59. (a) ; (b) At 8:21; about
2.5 miles
g1x 2= 24Ax -
1
4
Bf 1x 2= 7x
0
10
5
15
20
25
40
30
35
10 20 3025155
y
x
Chapter 2 Test
■
page 228
1. (a) 2 (b) 5 2. (a) is linear; f is not linear because it
has a term involving x
2
.
(b) (c) - 3
g
3. 4. (a) (b)
(c) 5. Vertical: ; horizontal;
6. (a) , y = 1 + 3x3x - y + 1 = 0
y =-8x = 6y =
5
2
x
y =
9
5
-
2
5
xy =-3 + 4xy =-3 +
1
2
x
1
0
2
y
x
1
0
2
y
x
A18 Answers to Selected Exercises and Chapter Tests
(b) , y = 3 - xx + y - 3 = 0
7. 10.5 in.
8. (a), (b) y = 5.667 + 0.413x
(c) 18 ounces
9. (a) (75, 200) (b) $75
Chapter 3
Algebra Checkpoint 3.1
■
page 255
1. (a) (b) (c) (d) 2. (a) (b)
(c) (d) 3. (a) (b) (c) (d)
4. (a) (b) (c) (d) 5. (a) 2
(b) 6 (c) 4 (d) 6. (a) x (b) (c) (d)
3.1 Exercises
■
page 256
1. (a) 200 bacteria (b) 1.8 (c) 0.8 (d) 80% 2. (a) 100 g
(b) 0.4 (c) (d) 3. (a) growth (b) decay
4. (a) decay (b) growth 6. , so they both have a
decay factor of . 7. (b), (c), and (d) 9. (a) Growth (b) 1.2
(c) 0.2 11. (a) Decay (b) (c) 13. (a) Decay
(b) 0.25 (c) 15. (a) Growth (b) 2.8 (c) 1.8
17. III 19. II 21. (a) 1.93 (b) 1.33 (c) 0.67 (d) 0.20
23. 100; 2 25. 27.
29. 31. 33.
35. (a) (b) 31 bacteria
37. (a)
f 1t 2= 1011.262
t
P = 350
#
11.7 2
x
P = 350
#
14 2
x
P = 350
#
10.65 2
x
P = 350
#
A
1
2
B
x
P = 350
#
14 2
x
- 0.75
-
2
3
1
3
1
3
3
-x
= A
1
3
B
x
- 60%- 0.6
1
x
2
y
3
9x
2
x
1>2
5
8
2
3
6
2
2
3
6
1
17
25
5
4>3
5
1>3
3
-1>2
3
1>2
y
8
z
2
25x
6
x
7
5
18
10
5
1
4
2
5
10
1
0
1
y
x
0
12
10
14
16
18
15 18 21 24
Regression
line
27
y
x
Year
Years since
2003
Salary
($)
2003 0 38,900.00
2004 1 39,678.00
2005 2 40,471.56
2006 3 41,280.99
2007 4 42,106.61
(b) (c) $44,683.87
(d)
S = 38,90011.022
t
43,000
38,000
0
4
x m(x)
0 10.0
1 5.0
2 2.5
3 1.25
4 0.625
5 0.3125
0
2
4
6
8
10
21435
y
x
39. (a) (b) $3940 in 1996, $6518 in 2005
41. (a) (b) 17.8 mg
43. (a) (b) $17,563
45. (a) (b) 0.0195 g
(c) (d)
m1x 2= 1010.5 2
x
E1x 2= 232,30010.911 2
x
A1t 2= 10010.75 2
t
E1x 2= 281311.183 2
x
m(x) decays exponentially
47. (a) 100,000 grey squirrels (b)
(c) 812,250 grey squirrels 49. (a)
(b)
A1x 2= 4510.5 2
x
P1x 2= 100,00012.85 2
x
50
0
4
Algebra Checkpoint 3.2
■
page 267
1. 2 2. 3. 2 4. 3 5. 25 6. 8 7. 64 8.
9. 1.50 10. 1.65 11. 21,450.46 12. 16,732.12
3.2 Exercises
■
page 267
1. (a) (b) (c) 2. principal, annual interest
rate, number of times compounded per year, number of years,
amount after t years 5. (a) (i) 4 (ii) 1.41 (b) (i) 10
(ii) 1.78 (c) (i) 0.75 (ii) 0.93 (d) (i) 0.6 (ii) 0.88
7. 0.13 9. 16% 11. 500; 0.76
13. (a) (b)
15. (a) (b)
17. 19.
21. 23.
25. (a) Type A: 1.69; Type B: 1.51 (b) Type A
27. (a) Type A: 1.25; Type B: 1.22 (b) Type A
P1t 2= 1000
#
10.77 2
t
P1t 2= 1000
#
10.25 2
t
P1t 2= 1000
#
11.06 2
t
P1t 2= 1000
#
12 2
t
P1t 2= 2000
#
11.59 2
t
2000
#
12 2
x
P1x 2=
P1t 2= 2000
#
18 2
t
2000
#
12 2
x
P1x 2=
A
1
2
B
1>h
b
1>5
a
3
25
9
1
3
Time (yr) Amount ($)
0 5000.00
1 5203.71
2 5415.71
3 5636.36
4 5865.99
5 6104.98
31. (a) $515.17 (b) $530.80 (c) $580.59
33. (a) $4263.83 (b) $4402.19 (c) $4545.05
35. (a) $3649.96 (b) $3656.98 (c) $3662.99
(d) $3664.17 37. 2.531% 39. 3.29% 41. Option (i)
43. (a) Location A: 1.685; Location B: 1.119 (b) Location A
45. (a) 10-year: 1.357, annual: 1.031
(b) (c) 1558 million
(d)
846
#
11.031 2
t
P1t 2=
1800
600
250
Answers to Section 3.3 A19
29.
47. (a) ; 0.99997 (b) 689.6 g
(c)
m1t 2= 700
#
10.99997 2
t
49. (a) 665,000 (b) 1.052;
(c) 2,362,000 51. (a)
(b)
A1t 2= 4510.63 2
t
n1t 2= 665000
#
11.052 2
t
3.3 Exercises
■
page 278
1. (a) varies (b) is constant (c) 400% 2. (a) is constant
(b) 200%, 2, 3 (c) 3. 20, 500 4. 25, 200
5. (a) True (b) True 7. (a) Exponential (b) Linear
(c) Exponential (d) Exponential
f 1x 2= 6
#
3
x
0
550
600
650
700
1000
2000 3000 4000 5000
y
t
50
0
6
m(t) decays exponentially.
Hour
t
Population
f 1t 2
Average
rate of
change
Percentage
rate of
change
0 30,000 — —
1 24,000
- 6000
- 20%
2 19,200
- 4800 - 20%
3 15,360
- 3840 - 20%
4 12,288
- 3072 - 20%
Hour
t
Population
f 1t 2
Average
rate of
change
Percentage
rate of
change
0 5000 — —
1 6500 1500 30%
2 8450 1950 30%
3 10,985 2535 30%
4 14,281 3296 30%
11.
13. (a) 27,000; 51,300; 97,470; 185,193; 90%, 90%, 90%, 90%
(b) Yes; y = 30,00011.92
x
0
50,000
100,000
150,000
200,000
250,000
300,000
400,000
350,000
2134
y
x
9.
0
5000
10,000
20,000
15,000
1
2 3 4
y
x
15. (a) ;
, (b) Yes; y = 20,00010.6 2
x
- 40%- 40%
- 40%, - 40%, - 8000, - 4800, - 2880, - 1728
17. (a) ;
(b) No
19. (a)
- 23.0%, - 29.8%, - 42.4%
- 18.7%,- 560, - 560, - 560, - 560
t
f 1t 2
0 200
1 350
2 500
3 650
4 800
t
g1t 2
0 200
1 350
2 613
3 1072
4 1876
(c) The world population levels off as it reaches 12 billion.
(d) 12 billion, yes
3.4 Exercises
■
page 291
1. (a) 5 (b) 25, 1, 2. (a) II (b) I 3. False 4. True
5.
1
25
14
500
0
0
20
80
40
60
_3 _2 _1
321
y
x
x
f 1x 2
- 3
1
216
- 2
1
36
- 1
1
6
0 1
1 6
2 36
3 216
A20 Answers to Selected Exercises and Chapter Tests
(c)
decreases to 0, while f
continues to decrease
indefinitely.
g
550
_500
g
f
4
0
21. (a) (b) ;
g1t 2= 50010.6 2
t
f 1t 2= 500 - 200t
t
f 1t 2
0 500
1 300
2 100
3
- 100
4
- 300
t
g1t 2
0 500
1 300
2 180.0
3 108.0
4 64.8
23. (a) Population A (b) Population B; 3000 (c) 100
25. (a) ; 1.56%
(b) (c) 0.103 billion, 0.108
billion; no (d) 1.56%,
1.56%; yes
f 1t 2= 6.45411.01562
t
(b) ;
(c)
increases much faster than
f does.
g
g1t 2= 20011.75 2
t
f 1t 2= 200 + 150t
1000
6
0
g
f
0
6.4
6.5
6.6
7.0
6.8
6.7
6.9
1
2 3 4
y
t
27. (a) 20,000 (b) ; 12% (c) 12%n1t 2= 2000011.122
t
Month
Salary
($)
Average rate
of change
0 10,000 —
1 11,000 1000
2 12,000 1000
3 13,000 1000
4 14,000 1000
5 15,000 1000
Offer A
Month
Salary
($)
Percentage
change
0 0.02 —
1 0.04 100%
2 0.08 100%
3 0.16 100%
4 0.32 100%
5 0.64 100%
Offer B
29. (a)
(b) ; linear (c) ;
exponential
(d) Offer A: $45,000, Offer B: $687,194,767.40; Offer B
31. (a) 100 (b) The population stabilizes at about 1200.
(c)
f
B
= 0.02122
t
f
A
= 10,000 + 1000t
From the graph it is
apparent that the population
of foxes increases
logistically, approaching a
carrying capacity of 1200.
(d) 1200, yes
33. (a) 11.79 billion; 11.97 billion
(b)
1400
40
0
Answers to Section 3.4 A21
7. 9.
0
10
40
20
30
25
_3 _2 _1
321
5
15
35
y
x
11. 13.
0
5
20
10
15
_3 _2 _1
321
y
s
0
2
4
6
8
10
_1
1
y
t
0
1
5
3
2
4
_3 _2 _1
321
y
x
15. 17.
14
0
1.5_1
a=8
a=
4
a=6
The smaller the value of a, the
steeper the graph of f is for
x 6 0.
The larger the value of a, the
steeper the graph of f is when
.x 7 0
3.0
0
2_2
a=0.5
a=0.9
a=0.7
19.
The larger the value of C,
the higher the graph of f.
21. 23. (a)
500
0
2_2
c=100
c=20
c=10
The smaller the value of C,
the lower the graph of f.
0
_30
2_2
C=_2
C=_3
C=_5
(b) Yes, (0, 1)
25. (a)
16
0
2_2
gf
(b) Yes, (0, 1)
27. (a) (b) The graph of
ultimately increases much
more quickly than that of f ;
(0.79, 5.17).
g
4
0
3_3
g
f
29. 31.
33. (a) Jim’s: ; Harold’s:
(b)
g1t 2= 2
#
8
t
f 1t 2= 100
#
8
t
f 1x 2= 8A
3
2
B
x
f 1x 2= 2
-x
60
0
3_1
g
f
140,000
6
0
g
f
The bacteria colonies have
different initial populations
but grow at the same rate.
(c) Jim: 26,214,400; Harold: 524,300
35. (a)
(c) Higher yearly returns result in a steeper graph.
(d) G.F.: $3543.12; B.F.: $2837.04; R.E.F.: $5130.33
9000
10
0
R
G
B
Yea r
Growth
fund value
($)
Bond
fund
value ($)
Real Estate
fund value
($)
2005 2000 2000 2000
2006 2200.00 2120.00 2340.00
2007 2420.00 2247.20 2737.80
2008 2662.00 2382.03 3203.23
(b) G.F.: ; B.F.: ;
R.E.F.: R1t 2= 200011.172
t
B1t 2= 200011.06 2
t
G1t 2= 200011.1 2
t
A22 Answers to Selected Exercises and Chapter Tests
37. (a) Annual rate 9%: ; annual rate 2%:
(b)
The smaller annual growth
rate results in a slower
increase in healthcare
expenditures.
g1t 2= 2.411.02 2
t
f 1t 2= 2.411.092
t
8
12
0
g
f
(c) 9% rate: $6.75 trillion, 2% rate: $3.04 trillion
3.5 Exercises
■
page 299
1.
2. a linear 3. an exponential 4. ;
6. If the growth factor is constant, then an exponential model is
appropriate. 7. (a), (c)
y = 10
#
3
x
y = 10 + 20x
x y
Average rate
of change
Percentage
rate of change
0 10 — —
1 30 20 200%
2 50 20 67%
3 70 20 40%
4 90 20 29%
5 110 20 22%
x y
Average rate
of change
Percentage
rate of change
0 10 — —
1 30 20 200%
2 90 60 200%
3 270 180 200%
4 810 540 200%
5 2430 1620 200%
(b) y = 12.0311.68622 2
x
2500
0
10
9. (a)
(b) Exponential;
(c)
f 1x 2= 209.1611.347652
x
1000
0
5
x
f 1x 2
Average rate
of change
Percentage
rate of change
0 210 — —
1 281 71 34%
2 379 98 38%
3 512 133 36%
4 689 177 33%
5 932 243 37%
11. (a)
(b) Linear;
(c)
f 1x 2= 440.7 - 48.171x
450
0
5
13. (a), (c)
x
f 1x 2
Average rate
of change
Percentage
rate of change
0 441 — —
1 392
- 49 - 11%
2 345
- 47 - 12%
3 296
- 49 - 14%
4 248
- 48
- 16%
5 200
- 48 - 19%
300
0
250
(b)
(d) 515.9 million
15. (a), (c)
f 1x 2= 6.0511.020412
x
200
0
25
(b)
(c) The doubling time is 10.75 h.
f 1x 2= 36.7811.06662842
x
Answers to Chapter 3 Review A23
17. (a)
Year x
Sales in year x ⴙ 1
Sales in year x
Growth
factor
2000 0 — —
2001 1
20.3>9.5
2.14
2002 2
35.0>20.3
1.72
2003 3
43.4>35.0
1.24
2004 4
85.0>43.4
1.96
2005 5
205.8>85.0
2.42
2006 6
254.5>205.8
1.24
2007 7
347.1>254.5
1.36
800
8
g
f
0
(b) 1.73 (c) (d)
(e)
g1x 2= 10.9411.6852
x
f 1x 2= 9.511.732
x
550
20
0
19. (a)
(b)
P1t 2=
500.9
1 + 49.1e
-0.498114t
t
f 1t 2
Average rate
of change
Percentage
rate of change
0 5000 — —
1 6000 1000 20%
2 7200 1200 20%
3 8640 1440 20%
Chapter 3 Review Exercises
■
page 306
1. (a) Growth (b) 1.25 (c) 25% (d) 1000
3. (a) Decay (b) (c) (d) 8
5. (a) (b) (c) 3200
7. (a) (b)
(c) 317 9. (a) $24,878.40 (b) $26,732.82
(c) $28,213.80 11. (a) (b) 296.77 kg
(c) (d)
13.
- 0.000433m1t2= 30010.9995672
t
m1t 2= 300A
1
2
B
t>1600
P1t 2= 132010.888 2
t
P1x 2= 132010.70 2
x
P1t 2= 20011.26 2
t
P1x 2= 200
#
2
x
- 40%
3
5
15. 17.
Increasing Decreasing
f 1t 2= 500011.22
t
0
1
4
2
3
_3 _2 _1
321
y
x
0
2
1
_3_4 _2 _1
4321
y
x
19. (0.28, 1.36)
10
0
2_1
gf
21.
23. (a), (c) (b) f 1t 2= 400.7711.0332 2
t
f 1x 2= A
2
3
B
x
600
350
100
25. (a) Avalon Acres:
800
6
0
400
6
0
Buccaneer Beach:
400
6
0
Coral Cay:
(b) Avalon Acres has exponential growth, Buccaneer Beach has
linear growth, and Coral Cay has logistic growth. (c) Avalon:
Buccaneer:
Coral: (d) (i) 20.18 (ii) 20.2%
(iii) 312
f 1x 2=
335.5
1 + 0.831
#
e
-0.446x
f 1x 2= 198.9 + 20.18xf 1x 2= 248.6211.202 2
x
(c) The population increases rapidly at first, then levels off at
about 500 flies.