Solution Manual for Elementary and Intermediate Algebra: Functions and Authentic Applications, 3rd Edition

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SOLUTIONSMANUALDIACRITECHELEMENTARY&INTERMEDIATEALGEBRA:FUNCTIONS ANDAUTHENTICAPPLICATIONSTHIRDEDITIONJay LehmannCollege of San Mateo

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iiiContentsChapter 1Introduction to Modeling1.1Variables and Constants11.2Scatterplots31.3Exact Linear Relationships51.4Approximate Linear Relationships8Chapter 1 Review Exercises12Chapter 1 Test15Chapter 2Operations and Expressions2.1Expressions182.2Operations with Fractions192.3Absolute Value and Adding Real Numbers222.4Change in a Quantity and Subtracting Real Numbers252.5Ratios, Percents, and Multiplying and Dividing Real Numbers282.6Exponents and Order of Operations31Chapter 2 Review Exercises34Chapter 2 Test38Cumulative Review of Chapters 1 and 240Chapter 3Using Slope to Graph Linear Equations3.1Graphing Equations of the Formsy=mx+bandx=a433.2Graphing Linear Models; Unit Analysis493.3Slope of a Line553.4Using Slope to Graph Linear Equations583.5Rate of Change65Chapter 3 Review Exercises71Chapter 3 Test77Chapter 4Simplifying Expressions and Solving Equations4.1Simplifying Expressions814.2Simplifying More Expressions834.3Solving Linear Equations in One Variable854.4Solving More Linear Equations in One Variable904.5Comparing Expressions and Equations984.6Formulas101Chapter 4 Review Exercises106Chapter 4 Test112Cumulative Review of Chapters 1–4115

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ivChapter 5Linear Functions and Linear Inequalities in One Variable5.1Graphing Linear Equations1205.2Functions1295.3Function Notation1315.4Finding Linear Equations1345.5Finding Equations of Linear Models1415.6Using Function Notation with Linear Models to Make Estimates and Predictions1475.7Solving Linear Inequalities in One Variable154Chapter 5 Review Exercises160Chapter 5 Test170Chapter 6Systems of Linear Equations and Systems of LinearInequalities6.1Using Graphs and Tables to Solve Systems1756.2Using Substitution to Solve Systems1816.3Using Elimination to Solve Systems1876.4Using Systems to Model Data1966.5Perimeter, Value, Interest, and Mixture Problems2026.6Linear Inequalities in Two Variables; Systems of Linear Inequalities in Two Variables211Chapter 6 Review Exercises219Chapter 6 Test233Cumulative Review of Chapters 1–6240Chapter 7Polynomial Functions and Properties of Exponents7.1Adding and Subtracting Polynomial Expressions and Functions2497.2Multiplying Polynomial Expressions and Functions2527.3Powers of Polynomials; Product of Binomial Conjugates2567.4Properties of Exponents2607.5Dividing Polynomials: Long Division and Synthetic Division262Chapter 7 Review Exercises267Chapter 7 Test271Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–7272Chapter 8Factoring Polynomials and Solving Polynomial Equations8.1Factoring Trinomials of the Formx2+bx+cand Differences of Two Squares2808.2Factoring Out the GCF; Factoring by Grouping2848.3Factoring Trinomials of the Formax2+bx+c2878.4Sums and Differences of Cubes; A Factoring Strategy2988.5Using Factoring to Solve Polynomial Equations3028.6Using Factoring to Make Predictions with Quadratic Models305Chapter 8 Review Exercises310Chapter 8 Test316Making Sure You’re Ready for Intermediate Algebra: A Review of Chapters 1–8318

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vChapter 9Quadratic Functions9.1Graphing Quadratic Functions in Vertex Form3279.2Graphing Quadratic Functions in Standard Form3339.3Simplifying Radical Expressions3429.4Using the Square Root Property to Solve Quadratic Equations3459.5Solving Quadratic Equations by Completing the Square3509.6Using the Quadratic Formula to Solve Quadratic Equations3579.7Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions3679.8Finding Quadratic Models3749.9Modeling with Quadratic Functions380Chapter 9 Review Exercises385Chapter 9 Test394Cumulative Review of Chapters 1–9399Chapter 10Exponential Functions10.1Integer Exponents40910.2Rational Exponents41310.3Graphing Exponential Functions41710.4Finding Equations of Exponential Functions42210.5Using Exponential Functions to Model Data428Chapter 10 Review Exercises435Chapter 10 Test440Chapter 11Logarithmic Functions11.1Composite Functions44411.2Inverse Functions44911.3Logarithmic Functions45611.4Properties of Logarithms45911.5Using the Power Property with Exponential Models to Make Predictions46411.6More Properties of Logarithms47211.7Natural Logarithms476Chapter 11 Review Exercises481Chapter 11 Test488Cumulative Review of Chapters 1–11491Chapter 12Rational Functions12.1Finding the Domains of Rational Functions and Simplifying Rational Expressions50212.2Multiplying and Dividing Rational Expressions; Converting Units50712.3Adding and Subtracting Rational Expressions51212.4Simplifying Complex Rational Expressions51912.5Solving Rational Equations52512.6Modeling with Rational Functions53612.7Proportions; Similar Triangles54112.8Variation543Chapter 12 Review Exercises547Chapter 12 Test558

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viChapter 13Radical Functions13.1Simplifying Radical Expressions56313.2Adding, Subtracting, and Multiplying Radical Expressions56613.3Rationalizing Denominators and Simplifying Quotients of Radical Expressions57013.4Graphing and Combining Square Root Functions57513.5Solving Radical Equations58013.6Modeling with Square Root Functions587Chapter 13 Review Exercises594Chapter 13 Test600Chapter 14Sequences and Series14.1Arithmetic Sequences60414.2Geometric Sequences60614.3Arithmetic Series61114.4Geometric Series614Chapter 14 Review Exercises616Chapter 14 Test619Cumulative Review of Chapters 1–14621Chapter 15Additional Topics15.1Absolute Value: Equations and Inequalities63315.2Performing Operations with Complex Numbers63715.3Pythagorean Theorem, Distance Formula, and Circles64115.4Ellipses and Hyperbolas64815.5Solving Nonlinear Systems of Equations657

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Chapter 1Introduction to ModelingHomework 1.12.In 2015, Chris Davis hit 47 home runs.4.In 2011, about 60 percent of children aged 5–18 participated in organized physical activity.6.In 2015, 11.1 percent of American workerswere in unions.8.The temperature is10 F−°. That is thetemperature is 10 degrees below 0 (inFahrenheit).10.The statement13t=represents the year 2018(13 years after 2005).12.The statement2t= −represents the year 2008(2 years before 2010).14.Answers may vary. Example:Lettbe the amount of time (in hours) that astudent prepares for an exam. Thentcanrepresent the numbers 0 and 4, buttcannotrepresent the numbers1−and3−.16.Answers may vary. Example:Letnbe the number of students enrolled in analgebra class. Thenncan represent thenumbers 15 and 28, butncannot represent thenumbers20−and 0.5.18.Answers may vary. Example:LetTbe the temperature (in degreesFahrenheit) in an oven. ThenTcan representthe numbers 300 and 450, butTcannotrepresent the numbers300−and450−.20.Answers may vary. Example:Letvbe the value (in thousands of dollars) ofa new home. Thenvcan represent the numbers100 and 250, butvcannot represent thenumbers100−and250−.22.a.Answers may vary. Example:9 inches4 inches12 inches3 inches18 inches2 inchesb.In the described situation, the symbolsWandLare variables. Their values canchange.c.In the described situation, the symbolAisa constant. Its value is fixed at 36 squareinches.24.a.Answers may vary. Example:4 inches4 inches5 inches3 inches6 inches2 inchesb.In the described situation, the symbolsWandLare variables. Their values canchange.c.In the described situation, the symbolPisa constant. Its value is fixed at 16 feet.26.a.Answers may vary. Example:2 inches1 inch4 inches2 inches6 inches3 inchesb.In the described situation, the symbolsW,L, andAare all variables. All of theirvalues can change.c.In the described situation, none of thesymbols are constants. All of their valuescan change.28.a.Answers may vary. Example:5 cm5 cm5 cm7 cm5 cm10 cm

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2ISM:Elementary and Intermediate Algebrab.In the described situation, the symbolsLandAare variables. Their values canchange.c.In the described situation, the symbolWisa constant. Its value is fixed at 5 cm.30.−8−7−6−5−4−3−2−1 0 1 2 3 4 5 67 832.−3−2−10123145494−012340.91.52.32.73.4−3−2−1012−2.4−0.70.20.938.The counting numbers between 1 and 5 are 2,3, and 4.1234540.The integers between4−and 4, inclusive, are4,3,2,1,−−−−0, 1, 2, 3, and 4.−5−4−3−2−101234542.The integers between6−and 3, inclusive, are6,5,4,3,2,1,−−−−−−0, 1, 2, and 3.−7−6 −5−4−3 −2−10123444.The positive integers between4−and 4 are 1,2, and 3.0123446.The integers in the list are4,−0, and 3.48.The rational numbers in the list are9.7,4,−−0,3 ,5and 3.50.The real numbers in the list are9.7,4,−−0,3 ,57,3, and.π52.Answers may vary. Example: 1, 5, and 1254.Answers may vary. Example:1,2,−−and3−56.Answers may vary. Example:13,,24and7958.Answers may vary. Example:2,5,andπ60.Answers may vary. Example:2,5,andπ62.20154122.455++++==The average number of songs downloaded pervisit is 2.4 songs.012345nNumber of songsAverage:2.4 songs64.798275777638977.855++++==The average percentage of flights in a year thatare on time is 77.8% per year.73747576777879808182 83pPercentAverage:77.8%66.1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7cPer person consumption68.−10−8−6−4−20246pAnnual profit (in millions)−5334.36.

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Chapter 1:Introduction to Modeling370.a.6.17.27.67.728.67.1544+++==The average sales are about $7.15 millionper year.b.Car sales increased from 2011 to 2014.Sales went up each year.c.The increases in car sales decreased from2011 to 2014. The decreases were:2011 to 20127.26.11.12012 to 20137.67.20.42013 to 20147.77.60.1−=−=−=YearsDecrease72.a.1719672763707455++++==The average number of cities where Uberoperates is about 74.b.The number of cities where Uber operatesincreased from 2010 to 2014. The numberof cities where Uber operates went up eachyear.c.The increases in the number of cities whereUber operates increased from 2010 to2014. The increases were2010 to 20117162011 to 201219782012 to 20136719482013 to 201427667209−=−=−=−=YearsIncrease74.No. Answers may vary. Example:The numbers 2 and 5 are not “between 2 and5.” The numbers between 2 and 5 are simply 3and 4.76.Two consecutive integers are 1 unit apart onthe number line.Two consecutive even integers are 2 unitsapart on the number line.Two consecutive odd integers are 2 units aparton the number line.78.Answers may vary. Example:90 points; the fifth score did not change theaverage, so it must be the same as the average.80.Answers may vary. Example:Negative quantities are graphed to the left of 0on the number line.Homework 1.22–16 even.yx−555(−1, 3)−5(2, 3)(1, 0)(3,−4)(−3.5, 1.5)(−5,−2)(−2.4,−4.1)(0,−4)18.They-coordinate is4−.20.Presumably, the longer a person works for acompany, the higher his or her salary will be.So, the salarysdepends on the number ofyearst. Thus,tis the independent variable andsis the dependent variable.22.As a student’s GPA increases, the percentageof college that would accept him or her wouldincrease. So, the percentagepdepends on theGPAg. Thus,gis the independent variableandpis the dependent variable.24.As the age of men increases, the percentagewith gray hair also increases. So, thepercentagepdepends on the agea. Thus,aisthe independent variable andpis thedependent variable.26.The longer the potato has been out of the oven,the cooler it will be (until it is cooledcompletely). So, the temperature of the potatoFdepends on the number of minutestsince itwas removed from the oven. Thus,tis the

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4ISM:Elementary and Intermediate Algebraindependent variable andFis the dependentvariable.28.The percentagepof people who owncomputers will change by agea. Thus,pis theindependent variable andais the dependentvariable.30.The total cost depends on the number of penspurchased. So,nis the independent variableandcis the dependent variable. The orderedpair (5, 10) means thatn= 5 andc= 10. Thecost of buying 5 pens is $10.32.The percentage of Internet users who usesocial networking sites depends on the numberof social networking sites. So,nis theindependent variable andpis the dependentvariable. The ordered pair (4,5) means thatn=4 andp= 5. So, 5% of Internet users use 4social networking sites.34.The number of ads in millions blocked byGoogle depends on the year. So, tis theindependent variable andnis the dependentvariable. The ordered pair (5, 780) means thatt= 5 andn= 780. In201052015+=, 780million ads were blocked by Google.36.The percentage of Americans who are satisfiedwith the size and influence of majorcorporations depends on the year. So,tis theindependent variable andpis the dependentvariable. The ordered pair()1,35−means thatt=1−andp= 35. In201512014−=, 35% ofAmericans felt satisfied with the size andinfluence of major corporations.38.yx−61218661240.PointAis 2 units to the left of the origin and 4units down. Thus, its coordinates are( 2,4)−−.PointBis 3 units to the left of the origin on thex-axis. Thus, its coordinates are( 3, 0)−.PointCis 5 units to the left of the origin and 4units up. Thus, its coordinates are( 5, 4)−.PointDis 4 units to the right of the origin and2 units up. Thus, its coordinates are(4, 2).PointEis 3 units below the origin on they-axis. Thus, its coordinates are(0,3)−.PointFis 3 units to the right of the origin and2 units down. Thus, its coordinates are(3,2)−.42.a.b.Answers may vary. Example: The averagelife span of a $100 bill is greater than theaverage life span of a $10 bill since $100bills are used less often than $10 bills.c.Answers may vary. Example: Each year,many more $10 bills are printed than $100bills since there is a larger demand for billswith lower value that tend to be used on amore regular basis.44.a.b.The total airline fuel cost was the least in2015. In 2015, the total airline fuel costwas $181 billion.c.The total airline fuel cost was the greatestin 2013. In 2013, the total airline fuel costwas $230 billion.d.No. Answers may vary. Example: The totalfuel cost may not be the greatest in thesame year as the average price per barrel ofcrude oil since total fuel cost depends onmany factors, including the types of planesthat were being utilized by airlines as wellas flight paths (distances various fleetsflew). Such factors would mean morebarrels of crude oil were being used.

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Chapter 1:Introduction to Modeling546.a.b.The average U.S. hourly pay increased. Ineach year, the average hourly pay wasgreater than the previous year.c.The five-year increase in the average U.S.hourly pay did not follow a pattern ofincrease or decrease.1995 to 200014.0311.672.362000 to 200516.1514.032.122005 to 201019.0616.152.912010 to 201521.0519.061.99−=−=−=−=YearsChangeFrom 1995 to 2005, the change in averageU.S. hourly pay decreased. However, from2005 to 2010, the change in average hourlypay increased.48.a.pa2040608040103020YearsPercentb.The highest point in the scatterplot is(21.0, 34). Answers may vary Example:It means that the 18–24 age group has thehighest percentage who are ordering moretakeout food than they did two years ago.c.The lowest point in the scatterplot is(70.0, 7). Answers may vary. Example:It means that the “over 64” age group hasthe lowest percentage who are orderingmore takeout food than they did two yearsago.d.The heights of the points decrease from leftto right. Answers may vary. Example:Younger age groups have higherpercentages than older age groups who areordering more takeout food than they didtwo years ago.50.a.pa2040608080206040YearsPercentageb.The 18–34 age group has the most faith insingle men raising children on their ownc.The “over 64” age group has the least faithin single men raising children on theirown.d.The percentages of adults of various agegroups who approve of single men raisingchildren on their own are decreasing as theage group increases. Therefore, thestudent's opinion based on the data iscorrect.52.a.Robin Ventura’s number of career grandslams is 18.b.The player who holds the record for thegreatest number of career grand slams isAlex Rodriguez with 25.c.The player who hit exactly 21 grand slamsis Manny Ramirez.54.The ordered pairs selected and scatterplotsmay vary. The points will lie on the samehorizontal line. Answers may vary.56.There are an infinite number of possibilitiesfor the positions of the other two vertices.Answers may vary. Example:(2, 3) and (7, 3); (2, 2) and (7, 2);(2, 10) and (7, 10);(2,2)−and(7,2)−.58.All points on a coordinate system with anx-coordinate of 0 make up they-axis.60.Answers may vary.Homework 1.32.The line contains the point(4,1)−, so1y= −when4x=.

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6ISM:Elementary and Intermediate Algebra4.The line contains the point( 6, 4)−, so6x= −when4y=.6.The line and they-axis intersect at(0, 1), sothey-intercept is(0, 1).8.The line contains the point(6, 1), so1y=when6x=.10.The line contains the point(3, 0), so3x=when0y=.12.The line and thex-axis intersect at(3, 0), sothex-intercept is(3, 0).14.a–b.yx−88204412−416c.The line contains the point(4, 14), so14y=when4x=.d.The line contains the point(8, 17), so8x=when17y=.e.The line and they-axis intersect at(0, 10),so they-intercept is(0, 10).f.The line and thex-axis intersect at( 10, 0)−, so thex-intercept is( 10, 0)−.16.a.The line contains the point (3, 1500), soB= 1500 whent= 3. This means thebalance 3 months after the account wasopened was $1500.b.The line contains the point (5, 500), sot= 5 whenB= 500. This means that5 months after the account was opened, thebalance was $500.c.The line and theB-axis intersect at(0, 3000), soB= 3000 whent= 0. Thismeans that the beginning balance of theaccount was $3000.d.The line and thet-axis intersect at (6, 0), sot= 6 whenB= 0. This means that theaccount will be empty after 6 months.18.Yes.yx20.a.yx246810826410b.No, there is not a linear relationshipbetweenxandy. The data points do not lieclose to one line.22.a.pt51015201604012080HoursDollarsb.The line contains the point (7, 56), sop= 56 whent= 7. This means thestudent’s pay for working 7 hours is $56.c.The line contains the point (12, 96), sot= 12 whenp= 96. This means that thestudent must work 12 hours to earn $96.

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Chapter 1:Introduction to Modeling724.a.st246840103020YearsThousands of dollarsb.The line contains the point (5, 30), sos= 30 whent= 5. We estimate thatperson’s salary will be $30 thousand afterhe has worked 5 years at the company.c.The line contains the point (7, 34), sot= 7whens= 34. We estimate that the personwill have worked 7 years at the companywhen his salary is $34 thousand.d.The line and thes-axis intersect at (0, 20),sos= 20 whent= 0. This means that theperson’s beginning salary at the companywas $20 thousand.26.a.b.The line contains the point (10, 2), sot= 10 whenp= 2. This means that thecompany’s annual profit will be $2 millionin the year 2005 + 10 = 2015.c.The line and thep-axis intersect at (0, 22),sop= 22 whent= 0. This means that thecompany’s annual profit was $22 millionin the year 2005.d.The line and thet-axis intersect at (11, 0),sot= 11 whenp= 0. This means that thecompany’s annual profit will be $0 in theyear 2005 + 11 = 2016.28.a.vt2468102051510YearsThousands of dollarsb.The line contains the point (8, 4), sov= 4whent= 8. This means that the car will beworth $4 thousand when it is 8 years old.c.The line contains the point (6, 8), sov= 8whent= 6. This means the value of the carwill be $8 thousand when it is 6 years old.d.The line and thev-axis intersect at (0, 20),sov= 20 whent= 0. This means that thevalue of the car was $20 thousand whennew.e.The line and thet-axis intersect at (10, 0),sot= 10 whenv= 0. This means that thecar will have no value after 10 years.30.a.b.The line contains the point (3, 21), sov= 21 whent= 3. This means the value ofthe stock was $21 in the year 2008.c.The line contains the point (10, 35), sot= 10 whenv= 35. This means the valueof the stock will be $35 in2005 + 10 = 2015.d.The line and thev-axis intersect at (0, 15),sov= 15 whent= 0. This means that thevalue of the stock was $15 in the year2005.pt2468102051510Years since 2000Millions of dollarsYears since 2005vt246840103020DollarsYears since 2000Years since 2005

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8ISM:Elementary and Intermediate Algebra32.a.at246816004001200800FeetMinutesb.The line contains the point (5, 800), soa= 800 whent= 5. This means the altitudeof the balloon is 800 feet after air has beenreleased for 5 minutes.c.The line contains the point (9, 0), sot= 9whena= 0. This means that it will take9 minutes for the balloon to reach theground.d.The prediction in part (c) will be anoverestimate. A faster decent the last400 feet means it will take less time toreach the ground than predicted.34.a.b.No, there is not a linear relationshipbetweentandp. The data points do not lieclose to one line.36.No. The3−is thex-coordinate of ordered pair()3, 4−, not thex-intercept.38.No. Thex-coordinate of ay-intercept must be0. They-intercept might be (0, 5), but not(5, 0).40.Yes. Any line that passes through the origin(0, 0) will have anx-intercept that is the sameas they-intercept. Answers may vary.Example:yx−555−5(0, 1)42.Answers may vary. Example:yx−555(0, 1)−544.Answers may vary. Example:Every point on they-axis has anx-coordinateof 0. So they-intercept of a line must have anx-coordinate of 0.46.Answers may vary. Example:A linear model is a line that describes therelationship between two quantities in anauthentic situation.Homework 1.4Throughout this section, answers may vary.2.a.yx−88844−8−4b.The variables are approximately linearlyrelated.c.Draw a line that comes close to the points.See the graph in part (a).d.Approximately( 1, 2.6)−e.Approximately( 6.2,3)−−f.Approximately (0, 3.7)12345678910 11 124812162024tpYears since 2000Percent delayed

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Chapter 1:Introduction to Modeling9g.Approximately( 3.4, 0)−4.a.The variablesxandyare approximatelylinearly related. The points in thescatterplot lie close to a line.b.Draw a line that comes close to the pointsto create the linear model as shown.c.A pizza with 30 carbohydrates has about290 calories. We performed interpolationbecause we used a part of the model whosex-coordinates are between thex-coordinates of two data points.d.A pizza with 450 calories has about 51carbohydrates. We performed interpolationbecause we used a part of the model whosex-coordinates are between thex-coordinates of two data points.e.The line in the scatterplot goes up from leftto right. Answers may vary. Example: Aline going up from left to right makessense because it shows that an increase inthe number of carbohydrates results in anincrease in the number of calories.6.a.b.The variablestandpare approximatelylinearly related. The points in thescatterplot lie close to a line.c.Draw a line that comes close to the pointsto create the linear model as shown.d.According to the model, 31% ofAmericans said there should be a ban onpossession of handguns around 2014.e.According to the model, about 27% ofAmericans will say there should be a banon possession of handguns in 2021.8.a.Note in the table below the difference int-values when calculatingtbased on yearssince 1990 as in problem #7 (1t) and yearssince 1985 as in problem #8 (2t). A modelusing2tvalues interpolatesnbetweent=7 andt= 30. A model using1tvaluesinterpolatesnbetweent= 2 andt= 25.12274.95104.610153.515203.120252.025302.1ttnb.Draw a line that comes close to the pointsto create the linear model. See the graph inpart (a).c.According to the model, the number ofcollisions in 2007 (t= 22) is about 2.8thousand. We performed interpolationbecause we used a part of the model whose

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10ISM:Elementary and Intermediate Algebrat-coordinates are between thet-coordinatesof two data points. The response here is thesame as in #7c. The value oftis differentthan in #7c, but the year itself has notchanged and therefore the value ofndoesnot change.d.According to the model, there will be 1.0thousand collisions by around 2020 (t=35). We performed extrapolation becausewe used a part of the model whoset-coordinates are not between thet-coordinates of two data points. That is, thefinal data value occurs att= 30, which issmaller than the value oftused to predictcollisions in 2020.The response here is thesame as in #8c. The value ofn(1.0thousand)has not changed. Sincencorrelates to a specific year (2020), theyear remains the same so the data valueremains unchanged.e.Thet-intercept (the point where the modelintersects thet-axis) is (43, 0). This means,according to the model, there will be nocollisions in 2028. Model breakdown haslikely occurred at this point and all yearsthat follow since it is unlikely that in anyyear there would be no collisions at all(and certainly not a negative number ofcollisions). Note that thet-intercept isdifferent than in #7e. It has shifted to theright by 5 compared with the value in #7e.The value oftmust change in order for thedata point “year 2028” and “0 collisions”to remain unchanged. The value oftconsistently increases or decreases by 5because we are calculating the values oftbased on time periods that are 5 yearsapart. Note that the actual data does notchange (that is, no matter the value oft, theyears still correspond to specific numbersof collisions). Only the reference points forcalculatingtchanges: (43, 0) represents 0collisions in 2028 just as (38, 0) did in #7e.10.a.b.Draw a line that comes close to the pointsto create the linear model. See the graph inpart (a).c.According to the model, the boiling pointof water at Mt. Everest’s peak (8850meters) is about160 F°.d.According to the model, the elevation atwhich a temperature of98.6 F°would feellike boiling water would be around 19thousand meters. We performedextrapolation because we used a part of themodel whoseE-coordinates are notbetween theE-coordinates of two datapoints.e.It takes more time to hard-boil eggs athigher altitudes. The heat that cooks theeggs comes from the boiling water. Sincethe temperature at which water boils islower, water vaporizes sooner, meaningthere is less actual water retaining heatinside the cooking pot. Therefore, itactually takes longer to hard-boil an egg ata higher altitude.12.a.b.Draw a line that comes close to the pointsto create the linear model. See the graph inpart (a).

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