High School Math Solution · animals for the rest of the day. Write an equation for the amount of money Antonio makes. ... Write an equation for the number of hours Tremaine actually

High SchoolMath Solution

Algebra I

Select Skills Practice for Review at Home

A1_SP_FM.indd FM-1A1_SP_FM.indd FM-1 24/04/19 3:46 PM24/04/19 3:46 PM

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ISBN: 978-1-934239-81-0Skills Practice

Printed in the United States of America1 2 3 4 5 6 7 8 9 CC 21 20 19 18 17


Module 2: Exploring Constant Change

Topic 2: Solving Linear Equations and Inequalities .............. 70

Topic 3: Systems of Equations and Inequalities ................... 92

Topic 4: Functions Derived from Linear Relationships ...... 116

Module 3: Investigating Growth and Decay

Topic 2: Using Exponential Equations ................................. 150

TABLE OF CONTENTS©

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Odd-numbered Answers ........................................... 240

70 • MODULE 2: Exploring Constant Change

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Topic 2

SOLVING LINEAR EQUATIONS AND INEQUALITIES

I. Modeling Rates of Change

A. Write a linear equation to model each problem situation and use the equation to answerthe question.

1. Autumn creates custom bracelets as a hobby and is planning to start selling them online for $10per bracelet. Autumn has already sold 5 custom bracelets. Her bracelets are so popular that sheexpects to sell every bracelet that she makes. Write an equation for the amount of money Autumnmakes. If Autumn makes an additional 24 bracelets, how much money will she make?

2. Antonio works at the circus making balloon animals, charging $3 for a balloon animal. Before hetook a lunch break at noon, he sold 14 balloon animals. After lunch, he goes back to selling balloonanimals for the rest of the day. Write an equation for the amount of money Antonio makes. Howmany balloon animals would Antonio need to sell after lunch to make $117 for the day?

3. Violet is trying to start an Intramural Club at her school. The principal tells her she must getsignatures from students to show support. Each fi lled sheet contains 25 signatures. By Monday,she and her friend already have 6 sheets fi lled with signatures. The principal tells Violet she musthave 7 more sheets fi lled with signatures. Write an equation for the number of signatures Violetwill get. If she fi lls all of these, how many signatures will she get in all?

4. Tremaine thought it would be okay to check his email, text, listen to music, and eat free food for1 hour of each of his shifts at Slow Food to Go. He lasted for 6 shifts, and then (to put it nicely)he was let go. Write an equation for the number of hours Tremaine actually worked. If Tremaineactually worked a total of 18 hours during his 6 shifts at Slow Food to Go, how many hours was hescheduled to work each shift?

Skills PracticeName Date

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SOLVING LINEAR EQUATIONS AND INEQUALITIES: Skills Practice • 71

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5. Dr. Betz, a vet, is running a free rabies clinic. He estimates that it will take him 12 minutes for eachanimal he treats. Dr. Betz has already seen 20 animals, the last of which was a shaggy dog. Write anequation for how many minutes Dr. Betz worked. How long did Dr. Betz work at the rabies clinic ifhe saw 20 more animals after the shaggy dog?

6. Nakida cleans the bird cages at an animal shelter. She doesn’t know how many birds were at theshelter this morning, but 4 adorable birds were adopted today. Each remaining bird has its owncage, each of which takes Nakida 3 minutes to clean. Write an equation for the amount of timeNakida spends cleaning cages. How long will it take to clean the cages if there were nine birds atthe shelter this morning?

II. Modeling Linear Equations Given Two Points

A. Determine the slope-intercept equation of each line given two points on the line.

1. (1, 23) and (22, 6) 2. (22, 4) and (4, 22)

3. (3, 9) and (1, 10) 4. (4, 27) and (211, 27)

5. (26, 1 __ 2 ) and (5, 3 __ 2 ) 6. (15, 0) and (21, 21)



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III. Modeling Linear Equations Given an Initial PointA. Write a linear equation to model each problem situation and use the equation to answerthe question.

1. An airplane prepares for landing. When it begins its descent towards the airport, the plane'saltitude is 27,000 feet. After descending at a steady rate for 6 minutes, its altitude is 19,000feet. Write an equation for the altitude of the plane. What will the altitude of the plane be afterdescending for 12 minutes?

2. A college freshman starts the year with $4400 in spending money and after 2 months, he has$3600 left. Assume that he continues to spend his money at this same rate. Write an equationfor the amount of spending money he has. How much money will he have left at the end of7 1 __ 2 months?

3. Taki and Connor invest $20 in drink mix, sugar, and paper cups for a lemonade stand. After 5hours, they have made $50 in profi ts. Assume that they sell the drinks at the same rate all day.Write an equation for their profi t for the day from the lemonade stand. If their stand continues tosell from 1:00 P.M. to 8:00 P.M. that day, what is their profi t for the day?

4. An experiment is underway to test the eff ect of extreme temperatures on a newly developedliquid. Two hours into the experiment, the temperature of the liquid is 220°C. After 6 hoursof the experiment, the temperature of the liquid is 240°C. Assume that the temperature hasbeen changing at a constant rate throughout the experiment and will continue to do so. Writean equation for the temperature of the liquid. How many hours into the experiment will thetemperature of the liquid be 2100°C?



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5. A baseball player starts the season with 77 career home runs. Ten games into the season, he hashit 2 home runs. Assume he continues at this pace. Write an equation for the number of careerhome runs he has hit. How many career home runs would you expect him to have at the end ofthe season (162 games)?

6. A man retires at age 50 with $605,000 in savings. He spends his savings at a steady rate, and after6 years of retirement, he has spent $300,000. Write an equation for the amount the man has insavings. When will he have $100,000 in savings?

IV. Solving Linear EquationsA. Solve each equation. Write the properties that justify each step.

1. 23(x 2 4) 5 29(x 2 1) 2. 8x 2 2(x 1 3) 5 4x 1 2

3. 22x 1 1 __________ 2 1 6 5 3x ___ 2 2 10 4. 12x 2 4( 1 __ 2 x 2 5) 5

1 __ 3 (6x 2 15)

5. 7(x 2 1) ________ 4 2 3 __ 4 5 28x 1

3__4 6. 24(2x 2 9) 1 6(2x 1 1) 5 28x 2 5(3x 2

6 __ 5 )



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B. Determine if the equation has one solution, no solution, or infi nite solutions. Show your work.

1. 22(x 2 3) 1 5 5 26(x 1 1) 1 4x

3. 20x 2 2(x 1 10) 5 2(5 2 2x)

2. 3x 1 1 ________ 2 1 6 5 1 __ 2 (3x 2 4) 1

17___2

4. 3 __ 5 (x 2 12) 5 24(x 1 9) 1 1

5. 27(x 2 1) 5 215x 1 8(x 1 2) 6. 8(x 2 3) ________ 2 1 5x 5 9(x 2 1) 2 3

V. Converting Literal EquationsA. Convert between degrees Fahrenheit and degrees Celsius using the literal equation given. Ifnecessary, round the answer to the nearest hundredth.

C 5 5 __ 9 (F 2 32)

1. 72°F 2. 211°F

3. 102.6°F 4. 25°C

5. 42°C 6. 23.4°C



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B. Convert each equation from standard form to slope-intercept form.

1. 4x 1 6y 5 48 2. 3x 2 5y 5 25

3. 24x 1 9y 5 45 4. 6x 2 2y 5 252

5. 2x 2 8y 5 96 6. 12x 1 28y 5 284

C. Convert each equation from slope-intercept form to standard form.

1. y 5 5x 1 8 2. y 5 24x 1 2

3. y 5 2 __ 3 x 2 6 4. y 5 2 1 __ 2 x 2 3

5. y 5 25x 2 13 6. y 5 3 __ 4 x 1 10



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D. Solve each equation for the variable indicated.

1. The formula for the area of a triangle is A 5 1 __ 2 bh. Solve the equation for h.

2. The formula for the area of a trapezoid is A 5 1 __ 2 (b1 1 b2)h. Solve the equation for b1.

3. The formula for the volume of a cylinder is V 5 pr2h. Solve the equation for h.

4. The formula for the volume of a pyramid is V 5 1 __ 3 lwh. Solve the equation for w.

5. The Ideal Gas Law is pV 5 nRT. Solve the equation for T.

6. Solve the literal equation 1 __ R 5 1 ___ R1

1 1 ___ R2 for R1.

7. Solve the literal equation a1 ___ a0

5 2 b1 ___ b0

for b0.

8. Solve the literal equation Z 5 4X ___ Y 2 1 3W for X.



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VI. Solving and Graphing InequalitiesA. Carlos works at an electronics store selling computer equipment. He can earn a bonus if he sells$10,000 worth of computer equipment this month. So far this month, he has sold $4000 worth ofcomputer equipment. He hopes to sell additional laptop computers for $800 each to reach his goal.The function f(x) 5 800x 1 4000 represents Carlos's total sales as a function of the number of laptopcomputers he sells.

3. less than $6000 4. at least $9000

5. more than $12,000 6. exactly $8000

Number of Laptop Computers Sold

Tota

l Sal

es (d

olla

rs)

x

y

10,000

8000

1 2 3 40

4000

12,000

2000

5 6 7 8 9

14,000

18,000

16,000

6000

1. at least $10,000 2. less than $7000

Use the graph to write an equation or inequality to determine the number of laptop computers Carlos would need to sell to earn each amount.



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B. Elena works at the ticket booth of a local playhouse. On the opening night of the play, tickets are$10 each. The playhouse has already sold $500 worth of tickets during a presale. The functionf(x) 5 10x 1 500 represents the total sales as a function of tickets sold on opening night.

Tickets Sold Opening Night

Tota

l Sal

es (d

olla

rs)

x

y

1000

800

10 20 30 400

400

1200

200

50 60 70 80 90

1400

1800

1600

600

Use the graph of the function to answer each question. Graph each solution on the number line.

1. How many tickets must Elena sell in order to make at least $1000?

2. How many tickets must Elena sell in order to make less than $800?

20100 30 40 50 7060 80 90 100

20100 30 40 50 7060 80 90 100


3. How many tickets must Elena sell in order to make at least $1200?

20100 30 40 50 7060 80 90 100


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C. Leon plays on the varsity basketball team. So far this season he has scored a total of 52 points. Hescores an average of 13 points per game. The function f(x) 5 13x 1 52 represents the total number ofpoints Leon will score this season. Write and solve an inequality to answer each question.

1. How many more games must Leon play in order to score at least 117 points?

2. How many more games must Leon play in order to score fewer than 182 points?

3. How many more games must Leon play in order to score more than 143 points?



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D. Draw an oval on the graph to represent the solution to each question. Write the correspondinginequality statement.

1. A hot air balloon at 4000 feet begins its descent. It descends at a rate of 200 feet per minute.The function f(x) 5 2200x 1 4000 represents the height of the balloon as it descends. How manyminutes have passed if the balloon is below 3000 feet?

Time (minutes)

Hei

ght (

feet

)

x

y

3000

50

2000

4000

1000

10 15

5000

6000

2. A bathtub fi lled with 55 gallons of water is drained. The water drains at a rate of 5 gallons perminute. The function f(x) 5 25x 1 55 represents the volume of water in the tub as it drains. Howmany minutes have passed if the tub still has more than 20 gallons of water remaining in it?

Time (minutes)

Volu

me

(gal

lons

)

x

y

30

50

20

40

10

10 15

90

80

70

60

50



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3. Lea is walking to school at a rate of 250 feet per minute. Her school is 5000 feet from her home. The function f(x) 5 250x represents the distance Lea walks. How many minutes have passed if Lea still has more than 2000 feet to walk?

Time (minutes)

Dis

tanc

e (fe

et)

x

y

3000

50

2000

4000

1000

10 15

4. Franco is riding his bike to school at a rate of 600 feet per minute. His school is 9000 feet from his home. The function f(x) 5 600x represents the distance Franco rides. How many minutes have passed if Franco has less than 3000 feet left to ride?

Time (minutes)

Dis

tanc

e (fe

et)

x

y

6000

50

4000

8000

2000

10 15



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E. Solve each inequality and then graph the solution on the number line.

1. 4x 1 3 # 3x 2 5

2. 22x . 6

3. 1 __ 8 (3x 2 16) , 4

4. x 2 3 ______ 2 $ 25



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5. 24(2 2 x) # 6(x 1 2)

6. 2 1 __ 2 (4x 1 20) , 27 (x 1 15 ___ 7 )

VII. Representing Compound InequalitiesA. Write each compound inequality in compact form.

1. All numbers less than or equal to 22 and greater than 24.

2. All numbers less than 55 and greater than 45

3. All numbers greater than or equal to 0 and less than or equal to 6.



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4. All numbers greater than 10 and less than 1000

5. All numbers less than or equal to 87 and greater than or equal to 83

6. All numbers greater than 21 and less than or equal to 39

B. Write an inequality for each graph.

1. 20 4 6 8 10–10 –8 –6 –4 –2

2. 210 3 4 5 76 8 9 10 11

3. 1 5 13 17 21 25 29 339 37

4. 20 4 6 8 10–10 –8 –6 –4 –2

5. 0 40 8–16 –12 –8 –4

6. 1612 20–4 0 4 8



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C. Graph each inequality.

1. 45 , x , 75

403530 45 50 55 6560 70 75 80 85 90 95 100

2. 25 , x , 5

–10–15 –5 0 5 10 15

3. 213 # x # 5

–10 0 10

4. 26 # x , 19

–10 0 10

5. 235 # x # 50

–50 –40 –20–30 –10 0 10 20 30 40 50

6. 25 , x # 45

–50 –40 –20–30 –10 0 10 20 30 40 50



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D. Write a compound inequality for each situation.

1. The fl owers in the garden are 6 inches or taller or shorter than 3 inches.

2. People with a driver's license are at least 16 years old and no older than 85 years old.

3. Kyle's car gets more than 31 miles per gallon on the highway or 26 miles or less per gallon inthe city.

4. The number of houses that will be built in the new neighborhood must be at least 14 and no morethan 28.

5. At the High and Low Store they sell high-end items that sell for over $1000 and low-end itemsthat sell for less than $10.

6. The heights of the twenty tallest buildings in New York City range from 229 meters to 381 meters.

E. Represent the solution to each part of the compound inequality on the number line. Then write thefi nal solution that is represented by each graph.

1. x . 2 and x # 7



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2. x . 10 or x . 6

3. x $ 5 or x , 3

4. x . 4 and x , 3

5. x # 21 or x . 0

6. 8 . x $ 28

7. x # 9 and x $ 2

8. x . 211 or x # 211



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F. Solve each compound inequality. Then graph and describe the solution.

1. 23 , x 1 7 # 17

2. 4 # 2x 1 2 , 12

3. x 1 5 . 14 or 3x , 9

4. 25x 1 1 $ 16 or x 2 6 # 28

5. 28 # 7 __ 8 x , 42

6. 22x 1 5 # 9 or 2x 2 13 . 231


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SYSTEMS OF EQUATIONS AND INEQUALITIES

I. Solving Systems of Linear Equations

A. Write a system of linear equations to represent each problem situation. Defi ne each variable.Then, graph the system of equations and estimate the point of intersection. Explain what the pointrepresents with respect to the given problem situation.

1. Eric sells model cars from a booth at a localfl ea market. He purchases each model carfrom a distributor for $12, and the fl ea marketcharges him a booth fee of $50. Eric sells eachmodel car for $20.

Number of Model Cars

Dol

lars

x

y

80

1 2 30

100

60

40

120

20

4 8 96 75

160

180

140

2. Ramona sets up a lemonade stand in frontof her house. Each cup of lemonade costsRamona $0.30 to make, and she spends $6on the advertising signs she puts up aroundher neighborhood. She sells each cup oflemonade for $1.50.

Cups of Lemonade

Dol

lars

x

y

6

1 2 30

3

9

4 8 96 75

12



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3. Chen starts his own lawn mowing business.He initially spends $180 on a new lawnmower.For each yard he mows, he receives $20 andspends $4 on gas.

Number of Yards Mowed

Dol

lars

x

y

160

2 4 60

200

120

80

240

40

8 16 1812 1410

320

360

280

4. Olivia is building birdhouses to raise moneyfor a trip to Hawaii. She spends a total of $30on the tools needed to build the houses. Thematerial to build each birdhouse costs $3.25.Olivia sells each birdhouse for $10.

Number of Birdhouses

Dol

lars

x

y

40

1 2 30

50

30

20

60

10

4 8 96 75

80

90

70


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5. The Spanish Club is selling boxes of fruit asa fundraiser. The fruit company charges theSpanish Club $7.50 for each box of fruit anda shipping and handling fee of $100 for theentire order. The Spanish Club sells each boxof fruit for $15.

Number of Fruit Boxes

Dol

lars

x

y

120

2 4 60

150

90

60

180

30

8 16 1812 1410

240

270

210

6. Jerome sells fl owers online for $12 perbouquet. Each bouquet costs him $5.70 tomake. Jerome also paid a one-time fee of $150to advertise his company.

Number of Bouquets

Dol

lars

x

y

160

3 6 90

200

120

80

240

40

12 24 2718 2115

320

360

280

B. Solve each system of equations by substitution. Determine whether the system is consistentor inconsistent.

1. y 5 2x 2 3 x 5 4

2. 2x 1 y 5 9 y 5 5x 1 2

3. y 5 3x 2 2 y 2 3x 5 4

4. 1 __ 2 x 1 3 __ 2 y 5 27

1 __ 3 y 5 2x 2 10

5. 0.8x 2 0.2y 5 1.5

0.1x 1 1.2y 5 0.8

6. 0.3y 5 0.6x 1 0.3

1.2x 1 0.6 5 0.6y


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C. Write a system of equations to represent each problem situation. Solve the system of equationsusing the linear combinations method.

1. The high school marching band is sellingfruit baskets as a fundraiser. They sell alarge basket containing 10 apples and 15oranges for $20. They sell a small basketcontaining 5 apples and 6 oranges for $8.50.How much is the marching band chargingfor each apple and each orange?

2. Asna works on a shipping dock at a tiremanufacturing plant. She loads a pallet with4 Mudslinger tires and 6 Roadripper tires.The tires on the pallet weigh 212 pounds.She loads a second pallet with 7 Mudslingertires and 2 Roadripper tires. The tires onthe second pallet weigh 184 pounds. Howmuch does each Mudslinger tire and eachRoadripper tire weigh?

3. The Pizza Barn sells one customer 3 largepepperoni pizzas and 2 orders of breadsticksfor $30. They sell another customer 4 largepepperoni pizzas and 3 orders of breadsticksfor $41. How much does the Pizza Barncharge for each pepperoni pizza and eachorder of breadsticks?

4. Nancy and Warren are making large potsof chicken noodle soup. Nancy opens4 large cans and 6 small cans of soup andpours them into her pot. Her pot contains115 ounces of soup. Warren opens 3 largecans and 5 small cans of soup. His potcontains 91 ounces of soup. How manyounces of soup does each large can and eachsmall can contain?

5. Taylor and Natsumi are making block towersout of large and small blocks. They arestacking the blocks on top of each other in asingle column. Taylor uses 4 large blocks and2 small blocks to make a tower 63.8 inchestall. Natsumi uses 9 large blocks and 4 smallblocks to make a tower 139.8 inches tall. Howtall is each large block and each small block?

6. Dave has 2 buckets that he uses to fi llthe water troughs on his horse farm.He wants to determine how many ounceseach bucket holds. On Tuesday, he fi llsan empty 2000-ounce water trough with7 large buckets and 5 small buckets of water.On Thursday, he fi lls the same empty watertrough with 4 large buckets and 10 smallbuckets of water. How many ounces doeseach bucket hold?


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D. Solve each system of equations using the linear combinations method.

1. 2.

3. 4.

5. 6.

7. 8.

3x 1 5y 5 82x 2 5y 5 22

4x 2 y 5 22x 1 2y 5 26

10x 2 6y 5 265x 2 5y 5 5

2x 2 4y 5 423x 1 10y 5 14

3x 1 2y 5 144x 1 5y 5 35

x 1 6y 5 112x 2 12y 5 10

1.5x 1 1.2y 5 0.60.8x 2 0.2y 5 2

3 __ 4 x 1 1 __ 2 y 5 2 3__4

2 __ 3 x 1 2 __ 3 y 5 2__3

E. Write a system of equations to represent each problem situation. Solve the system of equationsusing any method. Then, answer any associated questions.

1. Jason and Jerry are competing at aweightlifting competition. They are both liftingbarbells containing 200 pounds of plates(weights). Jason’s barbell has 4 large and 10small plates on it. Jerry’s barbell has 6 largeand 5 small plates on it. How much does eachlarge plate and each small plate weigh?

2. Rachel needs to print some of her digitalphotos. She is trying to choose betweenLightning Fast Foto and Snappy Shots.Lightning Fast Foto charges a base fee of $5plus an additional $0.20 per photo. SnappyShots charges a base fee of $7 plus anadditional $0.10 per photo. Determine thenumber of photos for which both stores willcharge the same amount. Explain which storeRachel should choose depending on thenumber of photos she needs to print.

3. Raja is trying to decide which ice cream shopis the better buy. Cold & Creamy Sundaescharges $2.50 per sundae plus an additional$0.25 for each topping. Colder & CreamierSundaes charges $1.50 per sundae plus anadditional $0.50 for each topping. Determinethe number of toppings for which bothvendors charge the same amount. Explainwhich vendor is the better buy depending onthe number of toppings Raja chooses.

4. Marcus is selling T-shirts at the State Fair. Hebrings 200 shirts to sell. He has long-sleevedand short-sleeved T-shirts for sale. On the fi rstday of the fair, he sells 1 __ 2 of his long-sleevedT-shirts and 1 __ 3 of his short-sleeved T-shirts for atotal of 80 T-shirts sold. How many of each typeof T-shirt did Marcus bring to the fair?


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5. Alicia has a booth at the fl ea market where shesells purses and wallets. All of her purses arethe same price and all of her wallets are thesame price. The fi rst hour of the day, she sells10 purses and 6 wallets for a total of $193. Thesecond hour, she sells 8 purses and 10 walletsfor a total of $183. How much does Aliciacharge for each purse and each wallet?

6. Weston wants to buy a one-yearmembership to a golf course. Rolling HillsGolf Course charges a base fee of $200and an additional $15 per round of golf.Majestic View Golf Course charges a basefee of $350 and an additional $10 perround of golf. Determine the number ofrounds of golf for which both golf coursescharge the same amount. Explain which golfcourse Weston should become a memberat depending on the number of rounds heintends to play.

7. Jun received two diff erent job off ers tobecome a real estate sales agent. DreamHomes off ered Jun a base salary of $20,000per year plus a 2% commission on all realestate sold. Amazing Homes off ered Jun abase salary of $25,000 per year plus a 1%commission on all real estate sold. Determinethe amount of real estate sales in dollars forwhich both real estate companies will payJun the same amount. Explain which off er Junshould accept based on the amount of realestate sales he expects to have.

8. Stella is trying to choose between two rentalcar companies. Speedy Trip Rental Carscharges a base fee of $24 plus an additionalfee of $0.05 per mile. Wheels Deals RentalCars charges a base fee of $30 plus anadditional fee of $0.03 per mile. Determinethe number of miles driven for which bothrental car companies charge the sameamount. Explain which company Stella shoulduse based on the number of miles sheexpects to drive.

9. Renee has two job off ers to be a door-to-doorfood processor salesperson. Pro ProcessProcessors off ers her a base salary of $15,000per year plus an additional $25 for eachprocessor she sells. Puree Processors off ersher a base salary of $18,000 per year plus anadditional $21 for each processor she sells.Determine the number of food processorsRenee would have to sell for both companiesto pay her the same amount. Explain whichjob off er Renee should accept based onthe number of food processors she expectsto sell.

10. Alex needs to rent a bulldozer. Smith’sEquipment Rentals rents bulldozers for adelivery fee of $600 plus an additional $37.50per day. Robinson’s Equipment Rentals rentsbulldozers for a delivery fee of $400 plus anadditional $62.50 per day. Determine thenumber of rental days for which both rentalcompanies charge the same amount. Explainwhich company Alex should choose basedon the number of days he expects to rent abulldozer.


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Topic 3


11. Serena has job off ers from two cardealerships. Classic Cars off ers her abase salary of $22,000 per year plusan additional 1% commission on all salesshe makes. Sweet Rides off ers her a basesalary of $13,000 per year plus an additional2.5% commission on all sales she makes.Determine the amount of car sales indollars for which both dealerships will paySerena the same amount. Explain whichoff er Serena should accept based on theamount of car sales she expects to have.

12. Dominique is trying to choose a satelliteinternet service provider. Reliable Satellitecharges customers a monthly fee of $26 plusan additional $0.30 per hour of online time.Super Satellite charges customers a monthlyfee of $18 plus an additional $0.50 per hourof online time. Determine the number ofhours of online time for which both providerscharge the same amount. Explain whichprovider Dominique should choose based onthe number of hours she expects to spendonline each month.

II. Graphing Linear Inequalities in Two Variables

A. Write a linear inequality in two variables to represent each problem situation.

1. Tanya is baking zucchini muffi ns and pumpkinmuffi ns for a school event She needs at least500 muffi ns for the event.

2. Hire needs to buy new pens and pencils forschool. Pencils cost $1 each and pens cost$2.50 each. He has $10 to spend.

3. Patti makes decorative fl ower pots. It costsher $20 to purchase the materials for each potShe wants to charge more than $6 per hour oflabor plus her materials cost for each pot.

4. Jose and Devon are working on a constructionjob together. Devon can put in 4 times asmany hours per week as Jose. Together theymust work at least 80 hours per week.

5. The Foxes are playing the Titans. TheTitans have been scoring 28 or more pointsper game this season. Between 7-pointtouchdowns and 3-point fi eld goals, the Foxesneed to score more than the Titan’s lowestscore to have a hope of winning the game.

6. Jack made twice his fundraising goal, whichwas less than the total that Cameron raised.Cameron raised $14 more than 5 times her goal.


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B. Tell whether the graph of each linear inequality will have a dashed line or a solid line.Explain your reasoning.

1. x 2 3y # 32 2. 8y 1 7x . 15

3. y , 14x 1 9 4. 25.2y 2 8.3x # 228.6

5. 2 __ 3 x 1 4 __ 9 y $ 3 6. y 2 17 . x 1 8

7. 185x 1 274y $ 65 8. 36 , 9y 2 2x

C. For each inequality, use the test point (0, 0) to determine which half-plane should be shaded.

1. 5x 1 7y . 213 2. y 2 30 # 9x 3. 28y . 6x 1 12

5. 31.9x 1 63.7y , 244.5

4. 46 $ 25y 1 10x

6. y 2 5 __ 6 . 1 __ 2 x 1 1__3

D. Graph each linear inequality.

1. y , 4x 1 2

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

2. y $ 10 2 x

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x


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3. y $ 1 __ 2 x 2 3

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

4. 2x 1 y . 1

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

5. 3x 2 4y $ 8

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

6. 3 __ 8 y 2 1 __ 4 x , 3__4

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x


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E. Graph each inequality and determine if the ordered pair is a solution for the problem situation.

1. Marcus has 50 tokens to spend at the schoolcarnival. The Ferris wheel costs 7 tokens andthe carousel costs 5 tokens. The inequality7x 1 5y # 50 represents the possible waysMarcus could use his tokens on the two rides.Is the ordered pair (6, 3) a solution for theproblem situation?

−8 −6 −4 −2−2

−4

2

Number of Ferris Wheel Rides

Num

ber

of C

arou

sel R

ides

0 4 6 8

−8

−6

8

6

4

2

y

x

2. Sophia has $2 to buy oranges and apples.Oranges cost $0.45 each and apples cost$0.25 each. The inequality 0.45x 1 0.25y # 2represents the possible ways Sophia couldspend her $2. Is the ordered pair (2, 3) asolution for the problem situation?

−8 −6 −4 −2−2

−4

2

Number of Oranges

Num

ber

of A

pple

s

0 4 6 8

−8

−6

8

6

4

2

y

x


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3. Noah plays football. His team’s goal is to scoreat least 15 points per game. A touchdownis worth 6 points and a fi eld goal is worth 3points. Noah’s league does not allow teams totry for the extra point after a touchdown. Theinequality 6x 1 3y $ 15 represents the possibleways Noah’s team could score points to reachtheir goal. Is the ordered pair (6, 21) a solutionfor the problem situation?

−8 −6 −4 −2−2

−4

2

Number of Touchdowns

Num

ber

of F

ield

Goa

ls

0 4 6 8

−8

−6

8

6

4

2

y

x

4. Lea has $5 to buy notebooks and pens.Notebooks cost $1.25 each and pens cost$0.75 each. The inequality 1.25x 1 0.75y # 5represents the possible ways Lea could spendher $5. Is the ordered pair (5, 2) a solution forthe problem situation?

−8 −6 −4 −2−2

−4

2

Number of Notebooks

Num

ber

of P

ens

0 4 6 8

−8

−6

8

6

4

2

y

x


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5. Leon has $10 to buy squash and carrots.Squash cost $1.50 each and carrots cost $2.75per bunch. The inequality 1.50x 1 2.75y # 10represents the possible ways Leon could spendhis $10. Is the ordered pair (22, 4) a solution forthe problem situation?

−8 −6 −4 −2−2

−4

2

Number of Squash

Num

ber

of B

unch

es o

f Car

rots

0 4 6 8

−8

−6

8

6

4

2

y

x

6. Olivia makes and sells muffi ns and scones ata school bake sale. She sells muffi ns for $0.50each and scones for $0.80 each. She hopesto raise at least $20. The inequality 0.50x1 0.80y $ 20 represents the possible waysOlivia could reach her goal. Is the ordered pair(20, 32) a solution for the problem situation?

−32 −16

−16

Number of Muffins

Num

ber

of S

cone

s0 16 32

−32

32

16

y

x

III. Systems of Linear InequalitiesA. Write a system of linear inequalities that represents each problem situation. Remember to defi neyour variables.

1. Jamal runs the bouncy house at a festival. The bouncy house can hold a maximum of 1200 poundsat one time. He estimates that adults weigh approximately 200 pounds and children under 16weigh approximately 100 pounds. For 1 four-minute session of bounce time, Jamal charges adults$3 each and children $2 each. Jamal hopes to make at least $24 for each session.


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2. Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 foradults and $5.50 for children. The theater expects to make at least $2000 for each showing.

3. The maximum capacity for an average passenger elevator is 15 people and 3000 pounds. It isestimated that adults weigh approximately 200 pounds and children under 16 weigh approximately100 pounds.

4. Pablo’s pickup truck can carry a maximum of 1000 pounds. He loads his truck with 20-pound bagsof cement and 80-pound bags of cement. He hopes to load at least 10 bags of cement into his truck.

5. Eiko is drawing caricatures at a fair for 8 hours. She can complete a small drawing in 15 minutesand charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges$25 for the drawing. Eiko hopes to make at least $200 at the fair.

6. Sofi a is making fl ower arrangements to sell in her shop. She can complete a small arrangement in30 minutes that sells for $20. She can complete a larger arrangement in 1 hour that sells for $50.Sofi a hopes to make at least $350 during her 8-hour workday.

7. A company is manufacturing two diff erent models of lamps, a table lamp and a fl oor lamp. A tablelamp takes 1 hour to make and a fl oor lamp takes 2 hours to make. The company has 9 employeesworking 8-hour days. The total manufacturing capacity is 40 lamps per day.


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B. Determine whether each given point is a solution to the system of linear inequalities.

1.

3.

5.

2x 2 y . 42x 1 y # 7

Point: (22, 210)

4x 1 y , 21 1 __ 2 x # 36 2 5y

Point: (3, 7)

15x 1 25y $ 30020x 1 30y # 480

Point: (14, 8)

2.

4.

6.

x 1 5y , 212y $ 23x 2 2

Point: (0, 21)

5x 1 3y . 622x 1 2y , 20

Point: (22, 6)

22.1x 1 7y $ 249.52y # 26.3x 1 78

Point: (10, 28)

C. Graph each system of linear inequalities and identify two solutions.

1.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y 2 3x , 5y 1 x . 3

2.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y . 2x 1 3y , 2x 2 5


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3.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y # 2 2 __ 3 x 1 3y $ 3x 2 4

4.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y , 2 1 __ 2 x 1 6y , 2x 1 1

5.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y $ 2 1 __ 3 x 1 4y $ 2x 1 5

6.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

y . 24x 1 8y , 24x 2 2


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D. Graph the solution set for each system of linear inequalities. Label all points of intersection of theboundary lines. Then determine a point that satisfi es all of the linear inequalities in the system.

1. y # 42x 2 y # 10y . 2x 2 4

2. y $ −2y # 4x 1 1 . yx 2 1 , y


3. y # 2 1 xy . x 2 12x 1 y $ 232x 1 1 . y

4. y . −2y # x 1 1−x # y 1 3y # −x 1 1y # 0

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5. y . −2y # 5x $ 23x # 1y . 3x 1 1

6. y # 3x + 2y , 4 2 x22x 1 3y # 23y $ 2x 2 8


1.

x

y

8

2 4 60

6

4

12

2

8 16 1812 1410

16

18

14

10

y $ 0 x $ 03x 1 y # 18x 1 3y # 30

2.

x

y $ 0 x $ 0

x 1 y # 204x 1 9y # 135

y

8

2 4 60

6

4

12

2

8 16 1812 1410

16

18

14

10

E. Graph the solution set for each system of linear inequalities. Label all points of intersection of theboundary lines.

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3.

x

y

40

10 20 300

30

20

60

50

10

40 80 9060 7050

80

90

70

y $ 15 x $ 103x 1 2y # 90 x 1 2y # 70

4.

x

y

40

10 20 300

30

20

60

50

10

40 80 9060 7050

80

90

70

y $ 10 x $ 20 x 1 y # 90x 1 4y # 240


5.

x

y

16

4 8 120

12

8

24

20

4

16 32 3624 2820

32

36

28

y $ 0 x $ 0 x 1 y # 26x 1 4y # 80

6.

x

x $ 10 x 1 5y # 1302x 1 5y # 150

y

16

4 8 120

12

8

24

20

4

16 32 3624 2820

32

36

28

y $ 14

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F. An electronics company is manufacturing electronic book readers. A basic model takes 4 hours and $40 to make. A touch screen model takes 6 hours and $120 to make. The company has 10 employees working 12-hour days. The daily operating budget is $1920 per day for materials. The company would like at least 3 basic models and 8 touch screen models produced per day. The system of linear inequalities represents the problem situation. The graph shows the solution set for the system of linear inequalities.

Let x represent the number of basic models.Let y represent the number of touch screen models.

x

y

8

2 4 60

6

4

12

10

2

8 16 1812 1410

16

18

14

(12, 12)

(3, 15)

(18, 8)(3, 8)

Basic Models

Touc

h Sc

reen

Mod

els

Analyze the solution set for the system of linear inequalities to answer each question.

y $ 8 x $ 3 4x 1 6y # 12040x 1 120y # 1920


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1. How many of each model should the company produce to minimize their daily cost?

2. How many of each model should the company produce to maximize the number of work hours utilized per day?

3. The company earns $30 for each basic model sold and $50 for each touch screen model sold. How many of each model should the company produce to maximize their profi t?

4. How many of each model would have to be produced to maximize the company’s daily cost?

5. How many of each model would have to be produced to minimize the number of work hours utilized per day?

6. During a special promotion, the company earns $20 for each basic model sold and $30 for each touch screen model sold. How many of each model should the company produce to maximize their profi t?



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FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPS

I. Analyzing Absolute Value Functions

A. Graph the function that represents each problem situation.

1. A jewelry company is making 16-inch beadnecklaces. The specifi cations allow for adiff erence of 0.5 inch. The functionf(x) 5 |x 2 16| represents the diff erencebetween the necklaces manufactured andthe specifi cations. Graph the function. Whatnecklace lengths meet the specifi cations?

Length of Necklace (inches)

Diff

eren

ce in

Len

gth

(inch

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

2. Julian is cutting lengths of rope for aclass project. Each rope length should be10 inches long. The specifi cations allowfor a diff erence of 1 inch. The functionf(x) 5 |x 2 10| represents the diff erencebetween the rope lengths cut and thespecifi cations. Graph the function. Whatrope lengths meet the specifi cations?

Rope Lengths (inches)

Diff

eren

ce in

Len

gth

(inch

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4



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3. A snack company is fi lling bags with pita chipssold by weight. Each bag should contain 8ounces of chips. The specifi cations allowfor a diff erence of 0.25 ounce. The functionf(x) 5 |x 2 8| represents the diff erencebetween the weight of a bag of chips andthe specifi cations. Graph the function. Whatweights meet the specifi cations?

Weight (ounces)

Diff

eren

ce in

Wei

ght (

ounc

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

4. A cereal company is fi lling boxes with cerealsold by weight. Each box should contain 32ounces of cereal. The specifi cations allowfor a diff erence of 0.5 ounce. The functionf(x) 5 |x 2 32| represents the diff erencebetween the weight of a box of cereal andthe specifi cations. Graph the function. Whatweights do not meet the specifi cations?

Weight (ounces)

Diff

eren

ce in

Wei

ght (

ounc

es)

x

y

0.8

4 8 120

1.0

0.6

0.4

1.2

0.2

16 32 3624 2820

1.6

1.8

1.4


5. Guests at the school harvest festival areasked to guess how many peanuts are in a jar. The jar contains 260 peanuts. All guests within 10 peanuts of the correct answer win a prize. The function f(x) 5 |x 2 260|represents the diff erence between a guess and the actual number of peanuts in the jar. Graph the function. What possible guesses will not win a prize?

Number of Peanuts Guessed

Diff

eren

ce b

etw

een

Gue

ss a

ndAc

tual

Num

ber

of P

eanu

ts

x

y

8

0

10

6

4

12

2

32080 160 240

16

18

14

6. The rules of an art contest state thatsculptures submitted should be 3 feet high but allow for a diff erence of 6 inches. The function f(x) 5 |x 2 3| represents the diff erence between a sculpture that is submitted and the specifi cations. Graph the function. What heights do not meet the specifi cations?

2 3Height of Sculpture (feet)

Diff

eren

ce in

Hei

ght (

feet

)

x

y

0.4

10

0.5

0.3

0.2

0.6

0.1

4

0.8

0.9

0.7

FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPS: Skills Practice • 119

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Name Date

II. Solving Absolute Value Equations and InequalitiesA. Match each compound inequality to its equivalent absolute value inequality.

1.a. 2 15 , 23x 1 7 , 15 |23x 1 7| # 15b. 23x 1 7 # 215 or 23x 1 7 $ 15 |23x 1 7| . 15c. 215 # 23x 1 7 # 15 |23x 1 7| , 15d. 23x 1 7 , 215 or 23x 1 7 . 15 |23x 1 7| $ 15

2.a. 22 # 6x 2 5 # 2 |6x 2 5| . 2b. 6x 2 5 , 22 or 6x 2 5 . 2 |6x 2 5| $ 2c. 6x 2 5 # 22 or 6x 2 5 $ 2 |6x 2 5| , 2d. 22 , 6x 2 5 , 2 |6x 2 5| # 2

3.a. 211 , 2x 2 10 , 11 |2x 2 10| . 11b. 2x 2 10 # 211 or 2x 2 10 $ 11 |2x 2 10| # 11c. 211 # 2x 2 10 # 11 |2x 2 10| , 11d. 2x 2 10 , 211 or 2x 2 10 . 11 |2x 2 10| $ 11

B. Solve the linear absolute value inequality by rewriting it as an equivalent compound inequality.Then graph your solution on the number line.

1. |x 2 3| $ 4

–6–8–10 –4 –2 0 42 6 8 10

2. 5 . |2x 1 7|

–6–8–10 –4 –2 0 42 6 8 10

3. |3x 2 1| . 11

–6–8–10 –4 –2 0 42 6 8 10

4. |2x 2 8| 2 1 # 3

–6–8–10 –4 –2 0 42 6 8 10



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5. |3x 2 2| , 24

–6–8–10 –4 –2 0 42 6 8 10

6. |24x 1 1| $ 9

–6–8–10 –4 –2 0 42 6 8 10

7. |22x 2 5| , 3

–6–8–10 –4 –2 0 42 6 8 10

8. 212 , |x 2 7|

–6–8–10 –4 –2 0 42 6 8 10

9. 2 1 |5x 2 4| # 18

–6–8–10 –4 –2 0 42 6 8 10

10. 10 . |x 2 3| 1 5

–6–8–10 –4 –2 0 42 6 8 10

11. |2x 1 4| $ 5

–6–8–10 –4 –2 0 42 6 8 10

12. |24x 1 8| 1 10 # 6

–6–8–10 –4 –2 0 42 6 8 10



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FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPSIII. Piecewise FunctionsA. Complete each table. Then, sketch a graph that represents the problem situation.

1. Rosa saved $100 to spend on vacation. For the fi rst 3 days of her vacation she spent $20 each day.Then for the next 2 days, she spent nothing. After those 5 days, she spent $10 each day until hersavings were depleted.

Time (days) Savings (dollars)

0

1

2

3

4

5

6

7

8

9Time (days)

Rosa’s Vacation Spending

Savi

ngs

(dol

lars

)

x

y

40

1 2 30

50

30

20

60

10

4 8 96 75

80

90

70


2. Belinda is saving money for a new snowboard. She earns $30 every 5 days she tutors. After 30days, she takes a break from tutoring and does not earn any money for 10 days. After those 10days she begins tutoring again and earns $30 every 5 days until she reaches her goal of $300.


0

5

10

15

20

25

30

35

40

45

50

55

60

Time (days)

Belinda’s Savings

Savi

ngs

(dol

lars

)

x

y

200

10 20 300

100

40 80 9060 7050

300


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Name Date

3. Shanise weighs 146 pounds when she starts a new exercise program. She loses 2 pounds in eachof the fi rst 4 weeks. Then, for the next 2 weeks she loses 1 pound per week. After those 2 weeksshe adds swimming to her program and again loses 2 pounds per week for the next 2 weeks.

Time (weeks) Weight (pounds)

0

1

2

3

4

5

6

7

8

Time (weeks)

Exercise Program Results

Wei

ght (

poun

ds)

x

y

140

0

130

150

1 2 3 4 8 96 75

4. Carlos is training for a bike race in 30 days. For the fi rst 5 days of his training he bikes 3 miles eachday. For the next 10 days he bikes 5 miles each day. For the next 10 days of his training he bikes 8miles each day. For the last 5 days of his training he bikes 10 miles a day.

Time (days) Total Distance (miles)

0

5

10

15

20

25

30

Time (days)

Carlos’s Bike Training

Tota

l Dis

tanc

e (m

iles)

x

y

100

20 300

50

150

10



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5. Maria earns money delivering newspapers each morning. For the fi rst 3 days she earns $18 eachday. For the next 2 days she takes on an additional route to cover a coworker who is out sick andearns $36 each day. For the next 2 days she returns to her original route and earns $18 each day.

Time (days) Earnings (dollars)

0

1

2

3

4

5

6

7

Time (days)

Maria’s Paper Route

Earn

ings

(dol

lars

)

x

y

72

1 2 30

90

54

36

108

18

4 8 96 75

144

162

126

6. Franco saved $200 to spend at an amusement park while on vacation. For the fi rst 2 days ofhis vacation he spent $36 each day. Then for the next 2 days, he spent nothing. After those4 days he stayed 3 more days and spent $40 each day.


0

1

2

3

4

5

6

7

Time (days)

Franco’s Vacation Spending

Savi

ngs

(dol

lars

)

x

y

100

0

50

150

1 2 3 4 8 96 75



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Name Date

B. Write a piecewise function to represent the data shown in each table.

1. x f(x)

0 60

1 55

2 50

3 45

4 45

5 45

6 45

7 43

8 41

9 39

2. x f(x)

0 0

2 3

4 6

6 9

8 12

10 12

12 12

14 18

16 24

18 30



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3. x f(x)

0 80

1 75

2 70

3 65

4 64

5 63

6 62

7 61

8 60

9 58

4. x f(x)

0 4

3 6

6 8

9 12

12 16

15 20

18 22

21 24

24 26

27 28



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3. A kids bounce house charges $8 for the fi rst hour and $2 for each additional hour of playtime. Write a function that represents the charges for up to 5 hours of playtime.

4. A fundraising company bases the profi t returned to organizations on the total value of products sold. The profi t returned is calculated as follows:

• $100 for sales more than $0 and up to and including $250,

• $225 for sales more than $250 and up to and including $500.

• $350 for sales more than $500 and up to and including $750, and

• $475 for sales more than $750 and up to and including $1000.

IV. Step FunctionsA. Write a step function to represent each problem situation.

1. To encourage quality and minimize defects, a manufacturer pays his employees a bonus based on the value of defective merchandise produced. The less defective merchandise produced, the greater the employee's bonus. The bonuses are calculated as follows:

• $50 for more than $0 and up to and including $100 of defective merchandise,

• $30 for more than $100 and up to and including $200 of defective merchandise,

• $10 for more than $200 and up to and including $300 of defective merchandise, and

• $0 for more than $300 of defective merchandise.

2. A jewelry store off ers reward coupons to its customers. A $2 reward coupon is awarded for each $20 spent. Write a function that represents the value of reward coupons awarded for up to $100 spent.



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Topic 4


Name Date

5. An ice rink charges hockey teams for ice time to practice. The ice rink charges $10 for the fi rst hour and $12 for each additional hour. Write a function that represents the charges for up to 5 hours.

6. Ava is participating in a walk for charity. Her sponsors agree to donate $2.50 plus $2.50 for each whole mile that she walks. Write a function that represents the donation amount for up to 5 miles.

V. Inverses of FunctionsA. Complete each table. Write an equation to represent the relationship. Write an equation for the inverse of the problem situation.

1. One foot is equivalent to 12 inches.

Feet Inches

1

2

3

4

5

2. One meter is equivalent to 100 centimeters.

Meters Centimeters

1

2

3

4

5

3. One pint is equivalent to 2 cups.

Pints Cups

2

4

6

8

10

4. Four quarters is equivalent to 1 dollar.

Quarters Dollars

4

16

32

64

128



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Topic 4


5. Three feet is equivalent to 1 yard.

Feet Yards

3

9

12

18

24

6. One U.S. dollar is equivalent to 13 Mexican pesos.

Dollars Pesos

1

2

3

4

5

B. Determine the inverse of each function. Graph the original function and its inverse.

1. f(x) 5 4x

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

2. f(x) 5 1 __ 3 x

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x



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Name Date

3. f(x) 5 2x 1 1

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

4. f(x) 5 26x 2 2

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

5. f(x) 5 2 __ 3 x 2 8

−32 −24 −16 −8−8

−16

80 16 24 32

−32

−24

32

24

16

8

y

x

6. f(x) 5 20.5x 1 9

−16 −12 −8 −4−4

−8

40 8 12 16

−16

−12

16

12

8

4

y

x



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5. Given that (1, 27) is a point on the graph of f(x), what is the corresponding point on the graph of its inverse?


C. Determine the corresponding point on the graph of the inverse of each function.






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150 • MODULE 3: Investigating Growth and Decay

Topic 2

USING EXPONENTIAL EQUATIONS

I. Identifying Exponential Growth or Decay

A. Determine if each type of account describes simple interest or compound interest based on the scenario given. Explain your reasoning.

1. Andrew deposits $300 into an account that earns 2% interest each year. After the fi rst year, Andrew has $306 in the account. After the second year, Andrew has $312 in the account, and after the third year, Andrew has $318 in the account.

3. Grace deposits $500 into an account that earns 2.5% interest each year. After the fi rst year, Grace has $512.50 in the account. After the second year, Grace has $525.31 in the account, and after the third year, Grace has $538.44 in the account.

2. Marilyn deposits $600 in an account that earns 1.5% interest each year. After the fi rst year, Marilyn has $609 in the account. After the second year, Marilyn has $618.14 in the account, and after the third year, Marilyn has $627.41 in the account.

4. Ty’Janet deposits $4000 into an account that earns 4.25% interest each year. After the fi rst year, Ty’Janet has $4170 in the account. After the second year, Ty’Janet has $4340 in the account, and after the third year, Ty’Janet has $4510 in the account.



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USING EXPONENTIAL EQUATIONS: Skills Practice • 151

Topic 2


Name Date

B. For each function, identify the y-intercept and interpret its meaning. Then, determine if the city’s population is increasing or decreasing.

5. Alma deposits $725 in an account that earns 3% interest each year. After the fi rst year, Alma has $746.75 in the account. After the second year, Alma has $768.50 in the account, and after the third year, Alma has $790.25 in the account.

6. Esh deposits $3500 in an account that earns 3.75% interest each year. After the fi rst year, Esh has $3631.25 in the account. After the second year, Esh has $3767.42 in the account, and after the third year Esh has $3908.70 in the account.

1. The function P(t) 5 4000 ? 1.03t represents the population of Millville as a function of time.

3. The function P(t) 5 10,525 ? 0.92t represents the population of Brasstown as a function of time.

5. The function P(t) 5 45,000 ? 1.004t represents the population of Wonder City as a function of time.

2. The function P(t) 5 8000 ? 0.98t represents the population of Grand City as a function of time.

4. The function P(t) 5 7210 ? 1.015t represents the population of Greenville as a function of time.

6. The function P(t) 5 109,375 ? 0.9995t represents the population of Lemonville as a function of time.


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II. Writing Exponential Functions

A. Write a function that represents each population as a function of time.

1. Bridge City has a population of 15,000 people. Its population is decreasing at a rate of 1.5% each year.

3. Hannonville has a population of 6075 people. Its population is decreasing at a rate of 0.5% each year.

5. Waterville has a population of 985 people. Its population is increasing at a rate of 0.65% each year.

2. Joyville has a population of 20,750 people. Its population is increasing at a rate of 2.7% each year.

4. Mapletown has a population of 95,000 people. Its population is decreasing at a rate of 1.375% each year.

6. Krystal City has a population of 40,500 people. Its population is increasing at a rate of 3.8% each year.


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Name Date

3. 4.

x y

0 1

1 3 __ 4

2 9 ___ 16

3 27 ___ 64

x y

0 21

2 24

4 216

6 264

1. 2.

x y

0 2

1 1

2 1 __ 2

3 1 __ 4

x y

0 1

2 25

4 625

6 15,625

B. Write the exponential function represented by the table of values.


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5.

x y

0 3

3 1 __ 9

6 1 ___ 243

9 1 ___ 6561

x y

0 22

1 2 1 __ 2

2 2 1 __ 8

3 2 1 __ 32

6.

1. 2 years

3. 15 years

2. 4 years

4. 20 years

III. Analyzing Exponential Functions

A. Cisco deposits $500 into a compound interest account. The interest rate for the account is 3.25%. The function P(t) 5 500 ? 1.0325t represents the balance in the account as a function of time. Determine the account balance after each given number of years.


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Topic 2


Name Date

B. Write a function to represent each problem situation.

1. Ronna deposits $500 into a compound interest account. The interest rate for the account is 4%.

3. Chen deposits $1200 into a compound interest account. The interest rate for the account is 3.5%.

5. Shen deposits $300 into a compound interest account. The interest rate for the account is 1.75%.

2. Leon deposits $250 into a compound interest account. The interest rate for the account is 6%.

4. Serena deposits $2700 into a compound interest account. The interest rate for the account is 4.25%.

6. Lea deposits $450 into a compound interest account. The interest rate for the account is 5.5%.

5. 50 years 6. 65 years


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IV. Solving Exponential Equations by Graphing

A. Use the intersection feature of your graphing calculator to answer each question.

1. For the function f(x) 5 6x 2 1, determine the value of x for which f(x) 5 7776.


5. For the function f(x) 5 23x 1 1, determine the value of x for which f(x) . 29.


4. For the function f(x) 5 2x 1 4, determine the value of x for which f(x) , 128.

6. For the function f(x) 5 5x 1 2, determine the value of x for which f(x) 5 15,625.


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Name Date

V. Modeling Exponential Functions

A. For each given data set determine the exponential regression equation and the value of the correlation coeffi cient, r. Round all values to the hundredths place.

1. 2.x y

10 5

20 6

30 8

40 15

50 32

60 70

70 150

x y

0 6000

1 2100

2 750

3 275

4 95

5 40

6 15

7 6

8 4

x 5 10 15 20 25 30 35 40

y 12 10 25 21 45 35 80 120

3.


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x 100 200 300 400 500 600 700

y 25.4 10.5 4.5 2.1 0.8 0.3 0.4

x 0 100 200 300 400 500 600

y 10 50 110 160 220 290 350

4.

6.

1. Tamara deposited $500 into a savings account in 1975. The table shows the value of Tamara’s savings account from 1975 to 2015. Predict the account’s value in 2025.

2. Tamika deposited $1000 into a savings account in 1980. The table shows the value of Tamika’s savings account from 1980 to 2010. Predict when the account’s value will be $5000.

x 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y 1200 585 272 126 42 40 14 12

Time Since 1975 (years) 0 5 10 15 20 25 30 35 40

Account Value (dollars) 500 650 900 1150 1600 2100 2750 3850 4800

Time Since 1980 (years) 0 5 10 15 20 25 30

Account Value (dollars) 1000 1200 1480 1800 2200 2720 3250

5.

B. Determine the exponential regression equation that models each situation. Use the equation to make the associated prediction. Round all values to the hundredths place.


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Name Date

3. A marine biologist monitors the population of sunfi sh in a small lake. He records 800 sunfi sh in his fi rst year, 600 sunfi sh in his fourth year, 450 sunfi sh in his sixth year, and 350 sunfi sh in his tenth year. Predict the population of sunfi sh in the lake in his sixteenth year.

5. Every hour, a scientist records the number of cells in a colony of bacteria growing in her lab. The sample begins with 15 cells. Predict the number of cells in the colony after 7 hours.

4. A marine biologist monitors the population of catfi sh in a small lake. He records 50 catfi sh in his fi rst year, 170 catfi sh in his fourth year, 380 catfi sh in his sixth year, and 1900 catfi sh in his tenth year. Predict when the population of catfi sh in the lake will be 6000.

6. Every hour, a scientist records the number of cells in a colony of bacteria growing in her lab. The sample begins with 50 cells. Predict how long it will take the sample to grow to 2000 cells.

Hour Number of Cells

0 15

1 40

2 110

3 300

4 850

Hour Number of Cells

0 50

1 90

2 160

3 290

4 530


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C. The scatter plot shows the registrations of plug-in electric vehicles in Norway over a period of time. The exponential regression equation that best fi ts the data is, p(x) 5 1018.99(2.05)x, where p(x) represents the number of registrations and x represents the number of years since 2010. The function is graphed on the grid. Analyze this information to answer each question.

Time Since 2010 (years)

Num

ber

of R

egis

trat

ions

x

y

30,000

1 2 3 40

20,000

40,000

10,000

5 6 7 8

60,000

50,000

1. Discuss any minimums and maximums as they relate to the problem situation.

2. Discuss the domain and range of the function as they relate to the problem situation.


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Name Date

3. Discuss the intervals of increase and decrease as they relate to the problem situation.

5. Predict the number of registrations of plug-in vehicles in Norway in 2017.

4. Discuss the x- and y-intercepts of the function as they relate to the problem situation.

6. Why might the number of registrations of electric plug-in vehicles be increasing exponentially?


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Topic 2

Solving Linear Equations and InequalitiesI. A.

1. y 5 10x 1 50; $290 3. y 5 25x 1 150; 325 signatures

5. y 5 12x 1 240; 480 minutes, or 8 hours

II. A.1. y 5 23x 3. y 5 2 1 __ 2 x 1 10 1__

2

5. y 5 1 __ 11 x 1 23__22

III. A.1. y 5 21333.33x 1 27, 000; 11,000 feet 3. y 5 14x 2 20; $78

5. y 5 1 __ 5 x 1 77; 109 career home runs

IV. A.1.

23(x 2 4) 5 29(x 2 1) 23x 1 12 5 29x 1 9 6x 1 12 5 9

6x 5 23x 5 2 1__

2

Distributive PropertyAddition Property of EqualitySubtraction Property of EqualityDivision Property of Equality

SOLVING LINEAR EQUATIONS AND INEQUALITIES: Skills Practice Answers • 259

A1_SP_AK_ODD.indd 259A1_SP_AK_ODD.indd 259 24/04/19 3:46 PM24/04/19 3:46 PM

Answer Key - ODD Numbers

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3. 22x 1 1 _________ 2 1 6 5 3x ___ 2 2 10

22x 1 1 1 12 5 3x 2 20 22x 1 13 5 3x 2 20 25x 1 13 5 220 25x 5 233 x 5 33 ___ 5

Multiplication Property of EqualityAssociative Property Subtraction Property of EqualitySubtraction Property of EqualityDivision Property of Equality

5. 7(x 2 1)

________ 4 2 3 __ 4 5 28x 1 3 ___ 4

7(x 2 1) 2 3 5 232x 1 3 7x 2 7 2 3 5 232x 1 3 7x 2 10 5 232x 1 3 39x 2 10 5 3 39x 5 13 x 5 1 ___ 3

Multiplication Property of EqualityDistributive Property Associative Property Addition Property of EqualityAddition Property of EqualityDivision Property of Equality

1. 22(x 2 3) 1 5 5 26(x 1 1) 1 4x 22x 1 6 1 5 5 26x 2 6 1 4x 22x 1 11 5 22x 2 6 11 Þ 26no solution

3. 20x 2 2(x 1 10) 5 2(5 2 2x) 20x 2 2x 2 20 5 25 1 2x 18x 2 20 5 25 1 2x 16x 5 15 x 5 15 ___ 16 one solution

5. 27(x 2 1) 5 215x 1 8(x 1 2) 27x 1 7 5 215x 1 8x 1 16 27x 1 7 5 27x 1 16 7 Þ 16no solution

IV. B.

V. A.1. C ≈ 22.22 3. C ≈ 39.22 5. F 5 107.6



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V. B.1. y 5 2 2 __ 3 x 1 8 3. y 5 4 __ 9 x 1 5 5. y 5 2 1 __ 8 x 2 12

V. C.

1. 25x 1 y 5 8 3. 22x 1 3y 5 218 5. 5x 1 y 5 213

V. D.

VI. A.1. 800x 1 4000 $ 10,000; x $ 8 3. 800x 1 4000 , 6000; x , 3

5. 800x 1 4000 . 12,000; x . 10

1. 2A ___ b 5 h 3. V ____ pr 2 5 h 5.

pV ___ nR 5 T 7. b0 5 2

a0b1____a1

VI. B.1. Elena must sell at least 50 tickets. x $ 50

20100 30 40 50 7060 80 90 100

3. Elena must sell at least 70 tickets. x $ 70

20100 30 40 50 7060 80 90 100

VI. C.

1. f(x) 5 13x 1 52117 # 13x 1 5265 # 13x

5 # x Leon must play in 5 or more games to scoreat least 117 points.

3. f(x) 5 13x 1 52143 , 13x 1 52

91 , 13x 7 , x

Leon must play in more than 7 games to score more than 143 points.



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VI. D.

1. More than 5 minutes have passed if theballoon is below 3000 feet. x . 5

Time (minutes)

Hei

ght (

feet

)

x

y

3000

50

2000

4000

1000

10 15

5000

6000

3. Less than 12 minutes have passed if Lea stillhas more than 2000 feet to walk. x , 12

Time (minutes)

Dis

tanc

e (fe

et)

x

y

3000

50

2000

4000

1000

10 15



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VI. E.1. x # 28

–12 –10 –6–8 –4 –2 0

5. x $ 210

–10–12 –8 –4–6 –2 0

3. x , 16

6 8 1210 14 16 18

VII. C.1.

403530 45 50 55 6560 70 75 80 85 90 95 100

5.

–50 –40 –20–30 –10 0 10 20 30 40 50

3.

–10 0 10

VII. A.1. 22 $ x . 24 3. 0 # x # 6 5. 87 $ x $ 83

VII. B.1. 28 , x # 11 3. 7 , x , 25 5. 214 # x # 5

VII. E.1.

2 , x # 7210 3 4 5 76 8 9 10

3.

x $ 5 or x , 3210 3 4 5 76 8 9 10

VII. D.1. x $ 6 or x , 3 3. x . 31 or x # 26 5. x . 1000 or x , 10



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5.

x # 21 or x . 0–3–4–5 –2 –1 0 21 3 4 5

7.

2 # x # 9210 3 4 5 76 8 9 10 11

VII. F.1.

Solution: 210 , x # 10–10 0 10

3.

Solution: x . 9 or x , 3210 3 4 5 76 8 9 10

5.

Solution: 32 # x , 4830 40 50



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Topic 3

Systems of Equations and InequalitiesI. A.

1. Eric’s income can be modeled by the equationy 5 20x, where y represents the income (indollars) and x represents the number ofmodel cars he sells. Eric’s expenses can bemodeled by the equation y 5 12x 1 50, wherey represents the expenses (in dollars) andx represents the number of model cars hepurchases from the distributor. y 5 20x y 5 12x 1 50

Number of Model Cars

Dol

lars

x

y

80

1 2 30

100

60

40

120

20

4 8 96 75

160

180

140

Expenses

Income

The break-even point is between 6 and 7 model cars. Eric must sell more than 6 model cars to make a profi t.

3. Chen's income can be modeled by theequation y 5 20x, where y represents theincome (in dollars) and x represents thenumber of yards he mows. Chen'sexpenses can be modeled by the equationy 5 4x 1 180, where y represents theexpenses (in dollars) and x represents thenumber of yards he mows.

y 5 20x y 5 4x 1 180

Number of Yards Mowed

Dol

lars

x

y

160

2 4 60

200

120

80

240

40

8 16 1812 1410

320

360

280Expenses

Income

The break-even point is between 11 and 12 yards mowed. Chen must mow more than 11 yards to make a profi t.

SYSTEMS OF EQUATIONS AND INEQUALITIES: Skills Practice Answers • 265


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5. The Spanish Club's income can be modeled bythe equation y 5 15x, where y represents theincome (in dollars) and x represents the numberof fruit boxes sold. The Spanish Club's expensescan be modeled by the equation y 5 7.50x 1 100,where y represents the expenses (in dollars) and xrepresents the number of fruit boxes ordered. y 5 15x y 5 7.50x 1 100

The break-even point is between 13 and 14 boxes of fruit. The Spanish Club must sell more than 13 boxes of fruit to make a profi t.

I. B.

1. The solution is (4, 5).

The system is consistent.

3. There is no solution.

The system is inconsistent.

5. The solution is (2, 0.5).

The system is consistent.

I. C.

1. Let x represent the amount charged for each apple. Let y represent the amount charged foreach orange.

10x 1 15y 5 20 10x 1 15y 5 20 5x 1 6y 5 8.50 22(5x 1 6y 5 8.50)

10x 1 15y 5 20210x 2 12y 5 217

3y 5 3y 5 1

The solution is (0.5, 1). The band charges $0.50 for each apple and $1.00 for each orange.

10x 1 15(1) 5 20 10x 1 15 5 20

10x 5 5x 5 0.5

Number of Fruit Boxes

Dol

lars

x

y

120

2 4 60

150

90

60

180

30

8 16 1812 1410

240

270

210

Expenses

Income



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3. Let x represent the charge for each pepperoni pizza. Let y represent the charge for each orderof breadsticks.

3x 1 2y 5 30 3(3x 1 2y 5 30) 4x 1 3y 5 41 22(4x 1 3y 5 41)

9x 1 6y 5 9028x 2 6y 5 282

x 5 8

The solution is (8, 3). The Pizza Barn sells each pepperoni pizza for $8 and each order of breadsticks for $3.

3(8) 1 2y 5 30 24 1 2y 5 30

2y 5 6y 5 3

5. Let x represent the height (in inches) of each large block. Let y represent the height (in inches)of each small block.

4x 1 2y 5 63.8 22(4x 1 2y 5 63.8) 9x 1 4y 5 139.8 9x 1 4y 5 139.8

28x 2 4y 5 2127.6 4(12.2) 1 2y 5 63.8 9x 1 4y 5 139.8 48.8 1 2y 5 63.8

x 5 12.2 2y 5 15y 5 7.5

The solution is (12.2, 7.5). Each large block is 12.2 inches tall and each small block is 7.5 inches tall.

I. D.

1. The solution is (6, 22). 3. The solution is (23, 24).

5. The solution is (0, 7). 7. The solution is (2, 22).

I. E.

1. Let x represent the weight (in pounds) of a large plate. Let y represent the weight (in pounds) of asmall plate. 4x 1 10y 5 200 6x 1 5y 5 200

The solution is (25, 10). Each large plate weighs 25 pounds. Each small plate weighs 10 pounds.



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Topic 3


3. Let x represent the number of toppings on a sundae. Let y represent the cost (in dollars) for asundae with x toppings.

y 5 0.25x 1 2.50 Cold & Creamy Sundaes y 5 0.50x 1 1.50 Colder & Creamier Sundaes

The solution is (4, 3.50). Both vendors charges $3.50 for a sundae with 4 toppings. It Raja wants fewer than 4 toppings, then Colder & Creamier Sundaes is the better buy. If Raja wants more than 4 toppings, Cold & Creamy Sundaes is the better buy.

5. Let x represent the charge for each purse. Let y represent the charge for each wallet.10x 1 6y 5 193

8x 1 10y 5 183

The solution is (16, 5.5). Alicia charges $16 for each purse and $5.50 for each wallet.

7. Let x represent the amount of Jun's real estate sales in dollars. Let y represent the yearly incomewhen Jun has x dollars in real estate sales.

y 5 0.02x 1 20,000 Dream Homes y 5 0.01x 1 25,000 Amazing Homes

The solution is (500,000, 30,000). Both real estate companies will pay Jun $30,000 per year for $500,000 in real estate sales. If Jun expects to sell less than $500,000 of real estate per year, than he should accept the off er from Amazing Homes. If Jun expects to sell more than $500,000 of real estate per year, then he should accept the off er from Dream Homes.

9. Let x represent the number of food processors sold. Let y represent Renee's yearly income whenshe sells x food processors.

y 5 25x 1 15,000 Pro Process Processors y 5 21x 1 18,000 Puree Processors

The solution is (750, 33,750). Both companies will pay Renee $33,750 for selling 750 food processors. If Renee expects to sell fewer than 750 food processors in one year, then she should accept the off er from Puree Processors. If Renee expects to sell more than 750 food processors in one year, than she should accept the off er from Pro Process Processors.

11. Let x represent the amount (in dollars) of cars sales. Let y represent the yearly income whenSerena has x dollars in car sales.

y 5 0.01x 1 22,000 Classic Cars y 5 0.025x 1 13,000 Sweet Rides

The solution is (600,000, 28,000). Both dealerships will pay Serena $28,000 for $600,000 in car sales. If Serena expects to have fewer than $600,000 in car sales in one year, then she should accept the off er from Classic Cars. If Serena expects to have more than $600,000 in car sales in one year, then she should accept the off er from Sweet Rides.



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II. A.1. x 1 y $ 500 3. y . 6x 1 20 5. 7x 1 3y . 28

II. B.1. The line will be solid because the symbol

is #.

5. The line will be solid because the symbolis $.

3. The line will be dashed because the symbolis ,.

7. The line will be solid because the symbolis $.

II. C.

1. The half-plane that includes (0, 0) should be shaded because the inequality is true for that point.

3. The half-plane that does not include (0, 0) should be shaded because the inequality is false forthat point.

5. The half-plane that does not include (0, 0) should be shaded because the inequality is false forthat point.

1.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

3.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

II. D.



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5.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

1.

−8 −6 −4 −2−2

−4

2

Number of Ferris Wheel Rides

Num

ber

of C

arou

sel R

ides

0 4 6 8

−8

−6

8

6

4

2

y

x

No. The ordered pair (6, 3) is not a solution to the inequality. It is not in the shaded half-plane.

3.

−8 −6 −4 −2−2

−4

2

Number of Touchdowns

Num

ber

of F

ield

Goa

ls

0 4 6 8

−8

−6

8

6

4

2

y

x

No. The ordered pair (6, 21) is not a solution for the problem situation. It is in the correct shaded half-plane, but it is not a reasonable answer because Noah's team cannot score a negative number of fi eld goals.

II. E.



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Topic 3


5.

−8 −6 −4 −2−2

−4

2

Number of Squash

Num

ber

of B

unch

es o

f Car

rots

0 4 6 8

−8

−6

8

6

4

2

y

x

No. The ordered pair (22, 4) is not a solution for the problem situation. It is in the correct shaded half-plane, but it is not a reasonable answer because Leon cannot purchase a negative number of squash.

III. A.1. x 5 the number of adults

y 5 the number of children 3x 1 2y $ 24 200x 1 100y # 1200

3. x 5 the number of adultsy 5 the number of children x 1 y # 15 200x 1 100y # 3000

5. x 5 the number of smalldrawingsy 5 the number of largedrawings8 hours 5 480 minutes 10x 1 25y $ 200 15x 1 45y # 480

7. Let t represent the numberof table lamps.Let f represent the numberof fl oor lamps.9 employees 3 8 hours perday 5 72 work hours per day

t $ 0 f $ 0

t 1 f # 40 t 1 2f # 72

9. Let t represent the numberof tablet computers. Let prepresent the number oflaptop computers.

t $ 0 p $ 0

t 1 p # 50 300t 1 600p # 20,000



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Topic 3


1.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

Answers will vary.(2, 3) and (6, 0)

3.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x


5.

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x


III. B.

III. C.

1. Yes. The point (22, 210) isa solution to the system ofinequalities.

3. No. The point (3, 7) is nota solution to the system ofinequalities.

5. No. The point (14, 8) is nota solution to the system ofinequalities.



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Topic 3


1.

−8 −6 −4 −2−2

−4

20 4 6

(2, –6)

(7, 4)(–8, 4)

8

−8

−6

8

6

4

2

y

x

Answers will vary.A solution to the system of inequalities would be (0, 0).

3.

−8 −6 −4 −2−2

−4

20 4 6

(–4, 5)

– , (1, 0)

8

−8

−6

8

6

4

2

y

x

53

13

– ,12

32

– , –23

53


5.

−8 −6 −4 −2−2

−4

20 4 6

(–3, 5)

(1, –2)(–1, –2)(–3, –2)

(–3, –8)

(1, 4)

(1, 5)

8

−8

−6

8

6

4

2

y

x

, 543


III. D.



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Topic 3


1.

x

y

8

2 4 60

6

4

12

2

8 16 1812 1410

16

18

14

10 (3, 9)(0, 10)

(6, 0)(0, 0)

3.

x

y

40

10 20 300

30

20

60

50

10

40 80 9060 7050

80

90

70

(10, 30)

(20, 15)(10, 15)

III. E.

5.

x

y

16

4 8 120

12

8

24

20

4

16 32 3624 2820

32

36

28

(8, 18)

(26, 0)

(0, 20)

(0, 0)

III. F.1. The minimum daily cost is $1080. To minimize their daily cost, the company should produce 3 basic

models and 8 touch screen models.

3. The maximum profi t is $960. To maximize their profi t, the company should produce 12 basicmodels and 12 touch screen models.

5. The minimum number of work hours utilized is 60 hours per day. To minimize the number of workhours utilized per day, the company should produce 3 basic models and 8 touch screen models.



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Topic 4


Topic 4

Functions Derived from Linear RelationshipsI. A.

1. The necklaces can be between 15.5 and 16.5inches long to meet the specifi cations.

Length of Necklace (inches)

Diff

eren

ce in

Len

gth

(inch

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

3. Each bags of chips can weigh between 7.75ounces and 8.25 ounces.

Weight (ounces)

Diff

eren

ce in

Wei

ght (

ounc

es)

x

y

0.8

2 4 60

1.0

0.6

0.4

1.2

0.2

8 16 1812 1410

1.6

1.8

1.4

5. A guess that is more than 270 or less than250 will not win a prize.

Number of Peanuts Guessed

Diff

eren

ce b

etw

een

Gue

ss a

ndAc

tual

Num

ber

of P

eanu

ts

x

y

8

800

10

6

4

12

2

160 320240

16

18

14

FUNCTIONS DERIVED FROM LINEAR RELATIONSHIPS: Skills Practice Answers • 275


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Topic 4


II. A.

1. a. |23x 1 7| , 15b. |23x 1 7| $ 15c. |23x 1 7| # 15d. |23x 1 7| . 15

3. a. |2x 2 10| , 11b. |2x 2 10| $ 11c. |2x 2 10| # 11d. |2x 2 10| . 11

II. B.

1. x 2 3 # 24 or x 2 3 $ 4x # 21 or x $ 7 –6–8–10 –4 –2 0 42 6 8 10

3. 3x 2 1 , 211 or 3x 2 1 . 11x , 2

10 ___ 3 or x . 4 –6–8–10 –4 –2 0 42 6 8 10

5. There is no solution. The absolute value can never be less than a negative number.

7. 23 , 22x 2 5 , 324 , x , 21 –6–8–10 –4 –2 0 42 6 8 10

9. 216 # 5x 2 4 , 1622 2 __ 5 # x # 4 –6–8–10 –4 –2 0 42 6 8 10

11. 2x 1 4 # 2 5 or 2 x 1 4 $ 5x # 2 1 or x $ 9 –6–8–10 –4 –2 0 42 6 8 10

III. A.

1. Time (days) Savings (dollars)

0 100

1 80

2 60

3 40

4 40

5 40

6 30

7 20

8 10

9 0Time (days)

Rosa’s Vacation Spending

Savi

ngs

(dol

lars

)

x

y

40

1 2 30

50

30

20

60

10

4 8 96 75

80

90

70



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Topic 4


3. Time (weeks) Weight (pounds)

0 146

1 144

2 142

3 140

4 138

5 137

6 136

7 134

8 132

Time (weeks)

Exercise Program Results

Wei

ght (

poun

ds)

x

y

140

0

130

150

1 2 3 4 8 96 75

5. Time (days) Earnings (dollars)

0 0

1 18

2 36

3 54

4 90

5 126

6 144

7 162 Time (days)

Maria’s Paper Route

Earn

ings

(dol

lars

)

x

y

72

1 2 30

90

54

36

108

18

4 8 96 75

144

162

126

III. B.

1. f (x) 5 { 25x 1 60, 0 # x # 3

45, 3 , x # 6 22x 1 57, 6 , x # 9

3. f (x) 5 { 25x 1 80,

0 # x # 3

2x 1 68, 3 , x # 8 22x 1 76,

8 , x # 9



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1. f ( x ) 5

⎧

⎪ ⎨ ⎪

⎩

50,

0 , x # 100

30,

100 , x # 200

10, 200 , x # 300

0,

300 , x

3. f (x) 5

⎧

⎪ ⎨ ⎪ ⎩

8,

0 , x # 1

10,

1 , x # 2

12, 2 , x # 3 14,

3 , x # 4

16,

4 , x # 5

5. f (x) 5

⎧

⎪ ⎨ ⎪ ⎩

10,

0 , x # 1

22,

1 , x # 2

34, 2 , x # 3 46,

3 , x # 4

58,

4 , x # 5

V. A.

1.

Feet Inches

1 12

2 24

3 36

4 48

5 60

Let f 5 the number of feet.

Let i 5 the number of inches.

i 5 12f

Inverse: f 5 i ___ 12

3.

Pints Cups

2 4

4 8

6 12

8 16

10 20

Let p 5 the number of pints.

Let c 5 the number of cups.

c 5 2p

Inverse: p 5 c ____ 2

5.

Feet Yards

3 1

9 3

12 4

18 6

24 8

Let f 5 the number of feet.

Let y 5 the number of yards.

y 5 f __ 3

Inverse: f 5 3y

IV. A.

Topic 4




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1. f 21(x) 5 x __ 4

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

f(x)

f –1(x)

3. f 21(x) 5 1 __ 2 x 2

1 __ 2

−8 −6 −4 −2−2

−4

20 4 6 8

−8

−6

8

6

4

2

y

x

f(x)

f –1(x)

V. B.

V. C.

5. f 21(x) 5 3 __ 2 x 1 12

−32 −24 −16 −8−8

−16

80 16 24 32

−32

−24

32

24

16

8

y

x

f(x)

f –1(x)

1. The corresponding point on the graph of the inverse is (5, 2).



Topic 4




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Topic 2


Topic 2

Using Exponential EquationsI. A.

1. This is a simple interest account because the interest earned at the end of each year is a percent of the original deposit amount.

3. This is a compound interest account because the interest earned at the end of each year is a percent of the account balance at the beginning of the year.

5. This is a simple interest account because the interest earned at the end of each year is a percent of the original deposit amount.

I. B.1. The y-intercept is 4000. This means that the current population of Millville is 4000 people.

The population of Millville is increasing.

3. The y-intercept is 10,525. This means that the current population of Brasstown is 10,525 people. The population of Brasstown is decreasing.

5. The y-intercept is 45,000. This means that the current population of Wonder City is 45,000 people. The population of Wonder City is increasing.

II. A.

1. P(t) 5 15,000 ? 0.985t 3. P(t) 5 6075 ? 0.995t 5. P(t) 5 985 ? 1.0065t

II. B.

1. f(x) 5 2 ( 1 __ 2 ) x

3. f(x) 5 ( 3 __ 4 ) x

5. f(x) 5 3 ( 1 __ 3 ) x

III. A.

1. In 2 years, the account balance will be $533.03.



III. B.1. P(t) 5 500 ? 1.04t 3. P(t) 5 1200 ? 1.035t 5. P(t) 5 300 ? 1.0175t



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Topic 2


IV. A.

1. For the function f(x) 5 6x 2 1, f(x) 5 7776 when x 5 6.

3. For the function f(x) 5 52x 1 1, f(x) 5 625 when x 5 23.

5. For the function f(x) 5 23x 1 1, f(x) . 29 when x , 1.

V. A.

1. f(x) 5 1.88(1.06)x

r 5 0.983. f(x) 5 6.91(1.07)x

r 5 0.955. f(x) 5 2101.58(0.25)x

r 5 20.99

V. B.

1. f(x) 5 497.63(1.06)x; The account’s value will be approximately $9166.42 in 2025.

3. f(x) 5 856.83(0.91)x; There will be approximately 189 sunfi sh in the lake in his sixteenth year.

5. f(x) 5 14.75(2.74)x; There will be approximately 17,102 bacteria cells in the colony after 7 hours.

V. C.

1. The function does not have a maximum value. Even though the given exponential function has no minimum value, the function as it relates to the problem has a minimum value of approximately 1019 in the year 2010.

3. The function increases over the entire domain from the year 2010 to infi nity.

5. When x 5 7, f(x) ≈ 155,041, so about 155,041 electric plug-in vehicles will be registered in 2017.

USING EXPONENTIAL EQUATIONS: Skills Practice Answers • 289


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