Solution Manual for College Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

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LEARNINGWORKSHEETSCOLLEGEMATHEMATICSFORBUSINESS,ECONOMICS,LIFESCIENCES,ANDSOCIALSCIENCESFOURTEENTHEDITIONRaymond A. BarnettMerritt CollegeMichael R. ZieglerMarquette UniversityKarl E. ByleenMarquette UniversityChristopher J. StockerMarquette University

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iiiContents1Linear Equations and Graphs11-1Linear Equations and Inequalities11-2Graphs and Lines51-3Linear Regression112Functions and Graphs152-1Functions152-2Elementary Functions: Graphs and Transformations192-3Quadratic Functions252-4Polynomial and Rational Functions392-5Exponential Functions532-6Logarithmic Functions593Mathematics of Finance693-1Simple Interest693-2Compound and Continuous Compound Interest753-3FV of an Annuity; Sinking Funds813-4PV of an Annuity; Amortization914Systems of Linear Equations; Matrices1034-1Review: Systems of Linear Equations in Two Variables1034-2Systems of Linear Equations and Augmented Matrices1114-3Gauss-Jordan Elimination1174-4Matrices: Basic Operations1254-5Inverse of a Square Matrix1294-6Matrix Equations and Systems of Linear Equations1334-7Leontief Input–Output Analysis1415Linear Inequalities and Linear Programming1475-1 and 5-2Systems of Linear Inequalities1475-3Linear Programming in Two Dimensions: A Geometric Approach1556Linear Programming: The Simplex Method1656-1The Table Method: An Introduction to the Simplex Method1656-2The Simplex Method: Maximization with ProblemConstraints of the Form≤1696-3The Dual Problem: Minimization with ProblemConstraints of the Form≥1756-4Maximization and Minimization with Mixed Problem Constraints1817Logic, Sets, and Counting1857-1Logic1857-2Sets1897-3Basic Counting Principles1937-4Permutations and Combinations1978Probability2018-1Sample Spaces, Events, and Probability2018-2Unions, Intersections, and Complement of Events; Odds2078-3Conditional Probability, Intersection, and Independence2138-4Bayes’ Formula2198-5Random Variables, Probability Distribution, and Expected Value225

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iv9Limits and the Derivative2299-1Introduction to Limits2299-2Infinite Limits and Limits at Infinity2359-3Continuity2419-4The Derivative2459-5Basic Differentiation Properties2519-6Differentials2579-7Marginal Analysis in Business and Economics26110Additional Derivative Topics26910-1The Constanteand Continuous Compound Interest26910-2Derivatives of Exponential and Logarithmic Functions27310-3Derivatives of Products and Quotients27710-4The Chain Rule28310-5Implicit Differentiation28910-6Related Rates29310-7Elasticity of Demand29711Graphing and Optimization30311-1First Derivatives and Graphs30311-2Second Derivatives and Graphs31111-3L’Hôpital’s Rule32311-4Curve-Sketching Techniques32711-5Absolute Maxima and Minima33311-6Optimization33912Integration34312-1Antiderivatives and Indefinite Integrals34312-2Integration by Substitution35112-3Differential Equations; Growth and Decay35912-4The Definite Integral36512-5The Fundamental Theorem of Calculus36913Additional Integration Topics37513-1Area Between Curves37513-2Applications in Business and Economics38113-3Integration by Parts38713-4Other Integration Methods39114Multivariable Calculus39714-1Functions of Several Variables39714-2Partial Derivatives40114-3Maxima and Minima40714-4Maxima and Minima Using Lagrange Multipliers41314-5Method of Least Squares41914-6Double Integrals over Rectangular Regions42714-7Double Integrals over More General Regions43115Markov Chains43715-1Properties of Markov Chains43715-2Regular Markov Chains44315-3Absorbing Markov Chains447

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College Mathematics: Learning WorksheetsChapter 11Name ________________________________ Date ______________ Class ____________Goal:To solve linear equation and linear inequalitiesIn Problems 1–3, solve for the variable:1.7822878222825828588288520520554xxxxxxxxxxx+=++−=+−+=+−=−===Section 1-1 Linear Equations and InequalitiesEquality Properties:1. Ifxyandais any real number, then.xaya2. Ifxyandais any nonzero real number, thenaxayand.xyaaInequality Properties:1. Ifxyandais any real number, then.xaya2. Ifxyandais any positive real number, thenaxayand.xyaa3. Ifxyandais any negative real number, thenaxayand.xyaaInterval Notation:A bracket, ] or [, is used if the endpoint is included.Aparentheses, ) or (, is used if the endpoint is not included.Infinity, either positive or negative, always uses a parentheses.

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College Mathematics: Learning WorksheetsChapter 122.73(611)16771833167253316725333316733252002520025258yyyyyyyyy3.81063668(6)10(6)6348260486012mmmmmmmm+=++=++=+=+−=In Problems 4–6, solve for the variable and place the final answer in interval notation.4.94229182(2,)xxx+>>>∞5.5211362123663[ 6,3)xxxx−< −+≤−< −≤>≥ −−≤<−6.353424123(12)125(12)34244961524212(12,)uuuuuuuu

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College Mathematics: Learning WorksheetsChapter 137.Break-even Analysis. A publisher for a promising new novel figures fixed costs(overhead, advances, promotion, copyediting, typesetting, and so on) at $87,000 and variablecosts (printing, paper, binding, shipping) at $4.50 for each book produced. If the book is soldto distributors for $28 each, how many must be produced and sold for the publisher to breakeven?Letx= the number of books produced. Since the break-even point is the point when cost isthe same as the revenue:2887, 0004.5023.5087, 0003702.12766xxxx=+==Therefore, the publisher must produce 3703 books to break even.

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College Mathematics: Learning WorksheetsChapter 15Name ________________________________ Date ______________ Class ____________Goal:To find the equations of lines,x-intercepts, andy-interceptsIn Problems 1–12, write the equation of the line in slope-intercept form with the givencharacteristics:1. Slope is 8 andy-intercept is (0, 3).Since the slope andy-intercept are given,83.yx=+2. Slope is –5 andy-intercept is (0,6).Since the slope andy-intercept are given,56.yx Section 1-2 Graphs and LinesSlope of a Line:2121,yymxx−=−where111:,Pxyand222:,PxySlope-Intercept Form of a Line:,ymxbwheremis the slope and (0,b) is they-intercept.Equation of a line in standard form:AxByC, whereAandBare not both zero.Horizontal Line:yb, slope is zero.Vertical Line:xa, slope is undefined.y-intercept: (0, b)x-intercept: (a,0)

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College Mathematics: Learning WorksheetsChapter 163. Slope is 37and passes through the point (–14, 2).11()32(( 14))73267387yym xxyxyxyx−=−−=− −−=+=+4. Slope is45and passes through the point (2, –3).11()4( 3)(2)5483554755yym xxyxyxyx 5. Passes through the points (4, 8) and (8, 4).21214841844yymxx−−−==== −−−11()81(4)8412yym xxyxyxyx−=−−= −−−= −+= −+6. Passes through the points (–1, 4) and (2, –2).212124622( 1)3yymxx  11()42(( 1))42222yym xxyxyxyx    

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College Mathematics: Learning WorksheetsChapter 177. Passes through the points (0, 6) and (5, 0).2121066505yymxx11()60(5)5665yym xxyxyx8. Passes through the points (0, –6) and (1, 0).21216066011yymxx−−−−====−−−11()06(1)66yym xxyxyx−=−−=−=−9. A horizontal line that passes through the point (–2, 8).A horizontal line is parallel to thex-axis and in the form,ybtherefore, the equationis8.y=10. A horizontal line that passes through the point (2, –5).A horizontal line is parallel to thex-axis and in the form,ybtherefore, the equationis5.y 11. A vertical line that passes through the point (–2, 7).A vertical line is parallel to they-axis and in the form,xatherefore, the equation is2.x= −12. A vertical line that passes through the point (2, –8).A vertical line is parallel to they-axis and in the form,xatherefore, the equation is2.x

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College Mathematics: Learning WorksheetsChapter 18In Problems 13–17, find thex-intercept and they-intercept.Solutions for thex-intercept will be found by settingy= 0, and they-intercepts willbe found by settingx= 0.13.33yx 14.22yx 15.112yx3(0)33yy 2(0)22yy  1 (0)121yy (0, 3)y-intercept(0, –2)y-intercept(0, –1)y-intercept033331xxx 022221xxx   10121122xxx (1, 0)x-intercept(–1, 0)x-intercept(2, 0)x-intercept16.443yx17.33xy 4 (0)434yy 0331yy (0, –4)y-intercept(0, 1)y-intercept40434433xxx 3(0)33xx  (3, 0)x-intercept(–3, 0)x-intercept

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College Mathematics: Learning WorksheetsChapter 1918. Graph each line in Problems 13–17.Graph for 13Graph for 14Graph for 15Graph for 16Graph for 17

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College Mathematics: Learning WorksheetsChapter 11019. A piece of equipment used in a landfill has an original value of $200,000. After twoyears of use, the piece of equipment is valued at $150,000.a) If the depreciation of the equipment is assumed to be linear, find an equation torelate the value (V) of the equipment over time (t).b) What would the value of the piece of equipment be after 6 years?c) In how many years would the value of the piece of equipment be $0?Solution:a)Since the value started at $200,000 and after two (2) years it was worth$150,000, the equipment depreciated as follows:150, 000200, 00050, 00025, 00022m−−=== −Since the slope is –25,000 and the equipment had a starting value of $200,000, theequation is25, 000200, 000.Vt= −+b)Substitute 6 in fort:25, 000200, 00025, 000(6)200, 000150, 000200, 00050, 000VtVVV= −+= −+= −+=Therefore, the equipment will be worth $50,000 after 6 years.c)Find the value oftwhenV= 0.25, 000200, 000025, 000200, 00025, 000200, 0008Vtttt= −+= −+==Therefore, the value will be $0 after 8 years.

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College Mathematics: Learning WorksheetsChapter 111Name ________________________________ Date ______________ Class ____________Goal:To interpret slopes and find linear regression equationsIn Problems 1–3, use the given information to answer the questions.1.Depreciation. A new car worth $45,000 is depreciating in value by $5000 per year.a)Find the linear model for the current value of the car,v, and the number ofyears,y, after it was purchased.b)Interpret the slope of the model.c)If the car is 3 years old, what does the model predict for its value?d)After how many years will the car be worth nothing?Solution:a)500045, 000vy= −+b)The value of the car decreases $5000 for every year after it was purchased.c)500045, 0005000(3)45, 00015, 00045, 00030, 000vyvvv= −+= −+= −+=The car is worth $30,000 after it is 3 years old.Section 1-3 Linear RegressionSolving Real-World Problems1.Construct a mathematical model.2.Solve the mathematical model.3.Interpret the solution.Linear Regression on a Graphing Calculator1.Enter the data in columnsL1andL2.2.In the “STAT” mode, find the “LinReg” function.3.Read the display to find the values of the slope and they-intercept.

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College Mathematics: Learning WorksheetsChapter 112d)500045, 0000500045, 000500045, 0009vyyyy= −+= −+==The car will be worth nothing after 9 years.2.Health Club Membership. A health club offers membership for a fee of $59 plus amonthly fee of $15 per month.a)Find the linear model for the membership fee,f, and the number of months,m,since you have been a member.b)Interpret the slope of the model.c)If you have been a member for 24 months, what does the model predict for thefee you have paid so far?d)After how many months will you have paid the health club $329?Solution:a)1559fm=+b)The fee will increase by $15 for every additional month of membership.c)155915(24)5936059419fmfff=+=+=+=The fee after 24 months will be $419.d)155932915592701518fmmmm=+=+==After 18 months, you will have paid $329 for your membership.

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College Mathematics: Learning WorksheetsChapter 1133.Stress.The table below shows the relationship between a stress test score and thediastolic blood pressure for 8 patients. A linear regression model for this data is0.5641.71,yx=+wherexrepresents the stress test score andyrepresents the blood pressure.Stress Test Score,x5562587892887580Blood Pressure,y7085728596908285a)Interpret the slope of the model.b)Use the model to predict the blood pressure for a person with a stress testscore of 75c)Use the model to estimate the stress test score for if the diastolic bloodpressure was 90.Solution:a)For every 1 point increase in the stress test score, the diastolic bloodpressure will increase by 0.56 points.b)0.5641.710.56(75)41.714241.7183.71yxyyyA person with a stress test score of 75 will have an approximate diastolicblood pressure of 84.c)0.5641.71900.5641.7148.290.5686.23yxxxxA person with a diastolic blood pressure of 90 will have a stress test scoreof approximately 86.

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