SOLUTIONS for
Elementary & Intermediate Algebra: Functions
TU
and Authentic Applications, 3rd edition
Author (s): Jay Lehmann
VI
A
AP
PR
O
VE
D
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, Chapter 1
Introduction to Modeling
ST
Homework 1.1 b. In the described situation, the symbols W
and L are variables. Their values can
2. In 2015, Chris Davis hit 47 home runs. change.
4. In 2011, about 60 percent of children aged 5– c. In the described situation, the symbol A is
18 participated in organized physical activity. a constant. Its value is fixed at 36 square
U
inches.
6. In 2015, 11.1 percent of American workers
were in unions. 24. a. Answers may vary. Example:
8. The temperature is −10°F . That is the
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temperature is 10 degrees below 0 (in 4 inches
Fahrenheit).
4 inches
10. The statement t = 13 represents the year 2018
(13 years after 2005). 3 inches
A
12. The statement t = −2 represents the year 2008 5 inches
(2 years before 2010). 2 inches
14. Answers may vary. Example: 6 inches
AP
Let t be the amount of time (in hours) that a
b. In the described situation, the symbols W
student prepares for an exam. Then t can
and L are variables. Their values can
represent the numbers 0 and 4, but t cannot
change.
represent the numbers −1 and −3 .
c. In the described situation, the symbol P is
16. Answers may vary. Example:
a constant. Its value is fixed at 16 feet.
Let n be the number of students enrolled in an
algebra class. Then n can represent the
PR
26. a. Answers may vary. Example:
numbers 15 and 28, but n cannot represent the
numbers −20 and 0.5. 1 inch 2 inches
2 inches
4 inches
18. Answers may vary. Example:
Let T be the temperature (in degrees
3 inches
Fahrenheit) in an oven. Then T can represent
the numbers 300 and 450, but T cannot 6 inches
O
represent the numbers −300 and −450 .
b. In the described situation, the symbols W,
20. Answers may vary. Example: L, and A are all variables. All of their
Let v be the value (in thousands of dollars) of values can change.
a new home. Then v can represent the numbers
VE
100 and 250, but v cannot represent the c. In the described situation, none of the
numbers −100 and −250 . symbols are constants. All of their values
can change.
22. a. Answers may vary. Example:
28. a. Answers may vary. Example:
4 inches
5 cm 5 cm
9 inches
D
5 cm 7 cm
3 inches
12 inches 5 cm
2 inches 10 cm
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18 inches
Copyright © 2019 Pearson Education, Inc.
, 2 ISM: Elementary and Intermediate Algebra
b. In the described situation, the symbols L 3
and A are variables. Their values can 50. The real numbers in the list are −9.7, −4, 0, ,
5
change.
7, 3, and π .
ST
c. In the described situation, the symbol W is
a constant. Its value is fixed at 5 cm. 52. Answers may vary. Example: 1, 5, and 12
30. 54. Answers may vary. Example: −1, −2, and −3
−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7 8
1 3 7
56. Answers may vary. Example: , , and
U
32. −5 1 9 2 4 9
4 4 4
58. Answers may vary. Example: 2, 5, and π
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−3 −2 −1 0 1 2 3 60. Answers may vary. Example: 2, 5, and π
34. 0.9 1.5 2.3 2.7 3.4
2 + 0 + 1 + 5 + 4 12
62. = = 2.4
5 5
0 1 2 3 4 The average number of songs downloaded per
A
visit is 2.4 songs.
36. −2.4 −0.7 0.2 0.9
Average:
2.4 songs
−3 −2 −1 0 1 2
AP
n
38. The counting numbers between 1 and 5 are 2, 0 1 2 3 4 5
3, and 4. Number of songs
79 + 82 + 75 + 77 + 76 389
1 2 3 4 5 64. = = 77.8
5 5
40. The integers between −4 and 4, inclusive, are The average percentage of flights in a year that
−4, − 3, − 2, − 1, 0, 1, 2, 3, and 4. are on time is 77.8% per year.
PR
Average:
77.8%
−5 −4 −3 −2 −1 0 1 2 3 4 5
42. The integers between −6 and 3, inclusive, are p
−6, − 5, − 4, − 3, − 2, − 1, 0, 1, 2, and 3. 73 74 75 76 77 78 79 80 81 82 83
Percent
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−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 66. c
1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7
44. The positive integers between −4 and 4 are 1,
2, and 3. Per person consumption
VE
68. −5 3
0 1 2 3 4
46. The integers in the list are −4, 0, and 3. p
−10 −8 −6 −4 −2 0 2 4 6
48. The rational numbers in the list are Annual profit (in millions)
3
−9.7, −4, 0, , and 3.
D
5
?
Copyright © 2019 Pearson Education, Inc.
, Chapter 1: Introduction to Modeling 3
6.1 + 7.2 + 7.6 + 7.7 28.6 74. No. Answers may vary. Example:
70. a. = = 7.15 The numbers 2 and 5 are not “between 2 and
4 4
The average sales are about $7.15 million 5.” The numbers between 2 and 5 are simply 3
ST
per year. and 4.
76. Two consecutive integers are 1 unit apart on
the number line.
Two consecutive even integers are 2 units
apart on the number line.
Two consecutive odd integers are 2 units apart
U
on the number line.
78. Answers may vary. Example:
b. Car sales increased from 2011 to 2014. 90 points; the fifth score did not change the
Sales went up each year.
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average, so it must be the same as the average.
c. The increases in car sales decreased from 80. Answers may vary. Example:
2011 to 2014. The decreases were: Negative quantities are graphed to the left of 0
Years Decrease on the number line.
A
2011 to 2012 7.2 − 6.1 = 1.1
Homework 1.2
2012 to 2013 7.6 − 7.2 = 0.4
2013 to 2014 7.7 − 7.6 = 0.1 2–16 even. y
5
1 + 7 + 19 + 67 + 276 370 (−1, 3) (2, 3)
AP
72. a. = = 74 (−3.5, 1.5)
5 5 (1, 0) x
The average number of cities where Uber −5 5
operates is about 74. (−5,−2)
(−2.4,−4.1) (3,−4)
−5
(0,−4)
18. The y-coordinate is −4 .
PR
20. Presumably, the longer a person works for a
company, the higher his or her salary will be.
So, the salary s depends on the number of
years t. Thus, t is the independent variable and
s is the dependent variable.
22. As a student’s GPA increases, the percentage
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b. The number of cities where Uber operates of college that would accept him or her would
increased from 2010 to 2014. The number increase. So, the percentage p depends on the
of cities where Uber operates went up each GPA g. Thus, g is the independent variable
year. and p is the dependent variable.
VE
c. The increases in the number of cities where 24. As the age of men increases, the percentage
Uber operates increased from 2010 to with gray hair also increases. So, the
2014. The increases were percentage p depends on the age a. Thus, a is
Years Increase the independent variable and p is the
2010 to 2011 7 −1 = 6 dependent variable.
2011 to 2012 19 − 7 = 8 26. The longer the potato has been out of the oven,
D
2012 to 2013 67 − 19 = 48 the cooler it will be (until it is cooled
2013 to 2014 276 − 67 = 209 completely). So, the temperature of the potato
F depends on the number of minutes t since it
was removed from the oven. Thus, t is the
?
Copyright © 2019 Pearson Education, Inc.
Elementary & Intermediate Algebra: Functions
TU
and Authentic Applications, 3rd edition
Author (s): Jay Lehmann
VI
A
AP
PR
O
VE
D
?
, Chapter 1
Introduction to Modeling
ST
Homework 1.1 b. In the described situation, the symbols W
and L are variables. Their values can
2. In 2015, Chris Davis hit 47 home runs. change.
4. In 2011, about 60 percent of children aged 5– c. In the described situation, the symbol A is
18 participated in organized physical activity. a constant. Its value is fixed at 36 square
U
inches.
6. In 2015, 11.1 percent of American workers
were in unions. 24. a. Answers may vary. Example:
8. The temperature is −10°F . That is the
VI
temperature is 10 degrees below 0 (in 4 inches
Fahrenheit).
4 inches
10. The statement t = 13 represents the year 2018
(13 years after 2005). 3 inches
A
12. The statement t = −2 represents the year 2008 5 inches
(2 years before 2010). 2 inches
14. Answers may vary. Example: 6 inches
AP
Let t be the amount of time (in hours) that a
b. In the described situation, the symbols W
student prepares for an exam. Then t can
and L are variables. Their values can
represent the numbers 0 and 4, but t cannot
change.
represent the numbers −1 and −3 .
c. In the described situation, the symbol P is
16. Answers may vary. Example:
a constant. Its value is fixed at 16 feet.
Let n be the number of students enrolled in an
algebra class. Then n can represent the
PR
26. a. Answers may vary. Example:
numbers 15 and 28, but n cannot represent the
numbers −20 and 0.5. 1 inch 2 inches
2 inches
4 inches
18. Answers may vary. Example:
Let T be the temperature (in degrees
3 inches
Fahrenheit) in an oven. Then T can represent
the numbers 300 and 450, but T cannot 6 inches
O
represent the numbers −300 and −450 .
b. In the described situation, the symbols W,
20. Answers may vary. Example: L, and A are all variables. All of their
Let v be the value (in thousands of dollars) of values can change.
a new home. Then v can represent the numbers
VE
100 and 250, but v cannot represent the c. In the described situation, none of the
numbers −100 and −250 . symbols are constants. All of their values
can change.
22. a. Answers may vary. Example:
28. a. Answers may vary. Example:
4 inches
5 cm 5 cm
9 inches
D
5 cm 7 cm
3 inches
12 inches 5 cm
2 inches 10 cm
?
18 inches
Copyright © 2019 Pearson Education, Inc.
, 2 ISM: Elementary and Intermediate Algebra
b. In the described situation, the symbols L 3
and A are variables. Their values can 50. The real numbers in the list are −9.7, −4, 0, ,
5
change.
7, 3, and π .
ST
c. In the described situation, the symbol W is
a constant. Its value is fixed at 5 cm. 52. Answers may vary. Example: 1, 5, and 12
30. 54. Answers may vary. Example: −1, −2, and −3
−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7 8
1 3 7
56. Answers may vary. Example: , , and
U
32. −5 1 9 2 4 9
4 4 4
58. Answers may vary. Example: 2, 5, and π
VI
−3 −2 −1 0 1 2 3 60. Answers may vary. Example: 2, 5, and π
34. 0.9 1.5 2.3 2.7 3.4
2 + 0 + 1 + 5 + 4 12
62. = = 2.4
5 5
0 1 2 3 4 The average number of songs downloaded per
A
visit is 2.4 songs.
36. −2.4 −0.7 0.2 0.9
Average:
2.4 songs
−3 −2 −1 0 1 2
AP
n
38. The counting numbers between 1 and 5 are 2, 0 1 2 3 4 5
3, and 4. Number of songs
79 + 82 + 75 + 77 + 76 389
1 2 3 4 5 64. = = 77.8
5 5
40. The integers between −4 and 4, inclusive, are The average percentage of flights in a year that
−4, − 3, − 2, − 1, 0, 1, 2, 3, and 4. are on time is 77.8% per year.
PR
Average:
77.8%
−5 −4 −3 −2 −1 0 1 2 3 4 5
42. The integers between −6 and 3, inclusive, are p
−6, − 5, − 4, − 3, − 2, − 1, 0, 1, 2, and 3. 73 74 75 76 77 78 79 80 81 82 83
Percent
O
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 66. c
1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7
44. The positive integers between −4 and 4 are 1,
2, and 3. Per person consumption
VE
68. −5 3
0 1 2 3 4
46. The integers in the list are −4, 0, and 3. p
−10 −8 −6 −4 −2 0 2 4 6
48. The rational numbers in the list are Annual profit (in millions)
3
−9.7, −4, 0, , and 3.
D
5
?
Copyright © 2019 Pearson Education, Inc.
, Chapter 1: Introduction to Modeling 3
6.1 + 7.2 + 7.6 + 7.7 28.6 74. No. Answers may vary. Example:
70. a. = = 7.15 The numbers 2 and 5 are not “between 2 and
4 4
The average sales are about $7.15 million 5.” The numbers between 2 and 5 are simply 3
ST
per year. and 4.
76. Two consecutive integers are 1 unit apart on
the number line.
Two consecutive even integers are 2 units
apart on the number line.
Two consecutive odd integers are 2 units apart
U
on the number line.
78. Answers may vary. Example:
b. Car sales increased from 2011 to 2014. 90 points; the fifth score did not change the
Sales went up each year.
VI
average, so it must be the same as the average.
c. The increases in car sales decreased from 80. Answers may vary. Example:
2011 to 2014. The decreases were: Negative quantities are graphed to the left of 0
Years Decrease on the number line.
A
2011 to 2012 7.2 − 6.1 = 1.1
Homework 1.2
2012 to 2013 7.6 − 7.2 = 0.4
2013 to 2014 7.7 − 7.6 = 0.1 2–16 even. y
5
1 + 7 + 19 + 67 + 276 370 (−1, 3) (2, 3)
AP
72. a. = = 74 (−3.5, 1.5)
5 5 (1, 0) x
The average number of cities where Uber −5 5
operates is about 74. (−5,−2)
(−2.4,−4.1) (3,−4)
−5
(0,−4)
18. The y-coordinate is −4 .
PR
20. Presumably, the longer a person works for a
company, the higher his or her salary will be.
So, the salary s depends on the number of
years t. Thus, t is the independent variable and
s is the dependent variable.
22. As a student’s GPA increases, the percentage
O
b. The number of cities where Uber operates of college that would accept him or her would
increased from 2010 to 2014. The number increase. So, the percentage p depends on the
of cities where Uber operates went up each GPA g. Thus, g is the independent variable
year. and p is the dependent variable.
VE
c. The increases in the number of cities where 24. As the age of men increases, the percentage
Uber operates increased from 2010 to with gray hair also increases. So, the
2014. The increases were percentage p depends on the age a. Thus, a is
Years Increase the independent variable and p is the
2010 to 2011 7 −1 = 6 dependent variable.
2011 to 2012 19 − 7 = 8 26. The longer the potato has been out of the oven,
D
2012 to 2013 67 − 19 = 48 the cooler it will be (until it is cooled
2013 to 2014 276 − 67 = 209 completely). So, the temperature of the potato
F depends on the number of minutes t since it
was removed from the oven. Thus, t is the
?
Copyright © 2019 Pearson Education, Inc.
