KARLA KARSTENS University of Vermont. Ronald J. Harshbarger University of South Carolina Beaufort. Lisa S. Yocco Georgia Southern University

Transcription

1 INSTRUCTOR S TESTING MANUAL KARLA KARSTENS University of Vermont COLLEGE ALGEBRA IN CONTEXT WITH APPLICATIONS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES SECOND EDITION Ronald J. Harshbarger University of South Carolina Beaufort Lisa S. Yocco Georgia Southern University Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

2 This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright 007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA All rights reserved. This manual may be reproduced for classroom use only. Printed in the United States of America. ISBN OPM Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

3 TABLE OF CONTENTS Chapter 1 Chapter Chapter Chapter 4 Chapter 5 Chapter 6 Functions, Graphs, and Models; Linear Functions...1 Quadratic and Other NonLinear Functions...7 Exponential and Logarithmic Functions.1 Higher-Degree Polynomial and Rational Functions...19 Systems of Equations and Matrices 5 Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus 1 Answers Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

4 ACKNOWLEDGEMENTS I would like to express my gratitude to Larry Kost, Helen Read, and Joe Kudrle for their technical assistance in creating this manual. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

5 Chapter 1 Test Form A 1 1. Determine the domain and range for each function. a. x f ( x ) b. 1 = x 8 y c. 1 f ( x) = x + 6. Graph each function with a graphing calculator using the standard viewing window. Determine the x- intercept(s) and y-intercept of each function, if they exist. a. y = x 4 b. y = x + 1 c. y = x 6x. Find the slope and y-intercept for each linear equation. a. y = 6x 1 b. 5x y = 15 1 c. y = x 4. Find the slope of a line through the given points. a. (-, 5) and (6, ) b. (, 4) and (-7, 4) c. (0, 6) and(-, -1) 5. The membership of a popular club from 1990 to 000 is given by the function N( x) = x + 18 people, x years after the club was founded in a. What is the membership of the club in 1995? b. Find and interpret the y-intercept of the function. c. Find the rate of change in the number of members in the club. 6. Write the equation of a line with the given characteristics: a. slope of and a y-intercept of 4 b. slope of - and passing through the point (6, 1) c. undefined slope and passing through the point (, 5) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

6 Chapter 1 Test Form A 7. Write the equation of a line through the point (1, 4) with the given characteristics: a. parallel to x + y = 6 1 b. perpendicular to y = x 4 c. perpendicular to the y-axis 8. Find f ( x + h) f ( x) h for f ( x) = x. 9. The table shows the number of books checked out from a village library by local residents from 1995 through Year Books (in thousands) a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after c. Use the unrounded model to predict the number of books that will be checked out of the library in Solve the systems of linear equations, if possible. x + y = 11 a. 4x y = 7 y = 5x + 9 b. x y = 7 y = x 8 c. 4x y = The cost to create a wind chime is given by C( x) = 14.5x dollars, when x wind chimes are made. The wind chimes sell for $50 each. Find the number of units that gives break-even for the wind chimes. 1. A job candidate is given the choice of two positions, one paying $4,00 per month and the other paying $,600 per month plus a 6% commission on all sales made during the month. What amount must the employee sell in a month for the second position to be more profitable? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

7 Chapter 1 Test Form B 1. Determine the domain and range for each function. a. x f ( x ) b. y = x 1 4 c. 5 f ( x) = x Graph each function with a graphing calculator using the standard viewing window. Determine the x- intercept(s) and y-intercept of each function, if they exist. a. y = 5x 1 b. y = x 1 c. y = x + 6x. Find the slope and y-intercept for each linear equation. a. y = 4x + 6 b. x + y = 6 c. y = 4 4. Find the slope of a line through the given points. a. (-, 6) and (6, 1) b. (, 9) and (-7, 5) c. (0, 6) and(-, -6) 5. The absorption of a certain drug into the body is given by A( x) = 0.084x grams, x hours after the drug was taken. a. How much of the drug is absorbed into the body hours after it was taken? b. Find and interpret the y-intercept of the function. c. What is the rate of change in the absorption of the drug into the body? 6. Write the equation of a line with the given characteristics: a. slope of and a y-intercept of - b. slope of -4 and passing through the point (, 1) c. undefined slope and passing through the point (-1, 1) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

8 4 Chapter 1 Test Form B 7. Write the equation of a line through the point (, 4) with the given characteristics: a. parallel to x + y = 6 1 b. perpendicular to y = x + 4 c. perpendicular to the y-axis 8. Find f ( x + h) f ( x) h for f ( x) = x The table shows the dividends per share of HWK, Inc. stock from 1990 through Year Dividends (in dollars) a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after c. Use the unrounded model to predict the dividends per share of HWK, Inc. for Solve the systems of linear equations, if possible. x y = 10 a. x + y = 10 y = x + 6 b. 4x y = y = x + 4 c. x y = The cost to create a bracelet is given by C( x) =.5x + 0 dollars, when x bracelets are made. The bracelets sell for $11 each. Find the number of units that gives break-even for the bracelets. 1. If Torrey has a course average score between 90 and 100, he will earn a grade of A in his algebra course. Suppose he has 4 exam scores of 88, 9, 85 and 9 and that the final exam score has twice the weight of the other four exams. What range of scores on the final exam will result in Torrey earning a grade of A? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

9 Chapter 1 Test Form C 5 1. Determine the domain and range for each function. a. x f ( x ) b. 1 = x + y c. f ( x) = x 6 4. Graph each function with a graphing calculator using the standard viewing window. Determine the x- intercept(s) and y-intercept of each function, if they exist. a. y = x 4 4 b. y = x + 1 c. y = x + 6x. Find the slope and y-intercept for each linear equation. a. y = x b. 5x + y = 15 c. y = 6 4. Find the slope of a line through the given points. a. (-, ) and (6, 1) b. (, 5) and (-, 5) c. (0, 4) and(-, -6) 5. Weekly sales of a new book at a book store are given by S( x) = 51x + books, x weeks after publication. a. How many books were sold 5 weeks after publication? b. Find and interpret the y-intercept of the function. c. Find the rate of change in the number of books sold per week. 6. Write the equation of a line with the given characteristics: a. slope of and a y-intercept of 5 b. slope of -1 and passing through the point (, 1) c. undefined slope and passing through the point (5, 1) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

10 6 Chapter 1 Test Form C 7. Write the equation of a line through the point (5, -) with the given characteristics: a. parallel to x + y = 6 1 b. perpendicular to y = x + 4 c. perpendicular to the y-axis 8. Find f ( x + h) f ( x) h for f ( x) = 4x The table shows the dividends per share of KSBW, Inc. stock from 1990 to Year Dividends (in dollars) a. Explain why a linear equation is a reasonable model for this data. b. Find the linear model that is the best fit for this data, with x equal to the number of years after c. Use the unrounded model to predict the dividends per share of KSBW, Inc. for Solve the systems of linear equations, if possible. x + y = a. x 4y = 6 y = 5x + 8 b. x y = 11 y = x + 4 c. x y = The cost to create a cutting board is given by C( x) = 15.4x + 50 dollars, for x cutting boards made. The cutting boards sell for $5 each. Find the number of units that gives break-even for the cutting board. 1. If Kenny has a course average score between 80 and 89, he will earn a grade of B in his algebra course. Suppose he has 4 exam scores of 76, 81, 8, and 77, and that the final exam score has twice the weight of the other three exams. What range of scores on the final exam will result in Kenny earning a grade of B? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

11 1. For each of the following functions, find the value of f (), if possible. 4 a. f ( x) = 8 x 4 + x 4, x < b. f ( x) = x + 6, x c. f ( x) = ( x ) + 6 d. f ( x) = x Find the coordinates of the vertex of the graph for each of the following. a. f ( x) = ( x 5) + 1 b. ( ) = f x x x Chapter Test Form A 7. The graph of ( ) ( 1) f x = x is shown below. a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. f ( x) = x x 15 b. f x x x ( ) = Given f ( x) = x and g( x) = x 5, find each of the following. a. ( f + g)() b. ( f g)( ) f c. ( fg)( ) d. (4) g 4 6. Given f ( x) = ( x + 1) and g( x) =, find each of the following. x a. ( f g)( ) b. ( g f )( x) 7. Find the inverse of f ( x) ( x 4) = Solve x Solve 4x 7 x 1 =. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

12 8 Chapter Test Form A 10. The profit from making and selling x units of a product is given by f ( x) = x 15x dollars. How many units should be produced and sold in order to make a profit of $1475? 11. The cost of a movie ticket, in dollars, depends on x, the age of the person attending the movie, and is described below by the piecewise function. 5, x < 1 C( x) = 7,1 x < 55 6, x 55 Find C(5) and interpret its meaning in the context of the problem. 1. The population of a certain city is given in the following table. Year Population 796, ,400 90,50 914, ,00 750,870 57,18 a. Using an input equal to the number of years after 190, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in c. If the population continues according to the model, when will the population of the city be 500,000 people? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

13 1. For each of the following functions, find the value of f (5), if possible. 4 a. f ( x) = 8 x 4 + x 4, x < b. f ( x) = x + 6, x c. f ( x) = ( x ) + 6 d. f ( x) = x Find the coordinates of the vertex of the graph for each of the following. a. f ( x) = 6( x + 4) b. ( ) = f x x x Chapter Test Form B 9. The graph of f ( x) 8 x = is shown below. a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. f ( x) = x + 4x 1 b. f x x x ( ) = Given f ( x) = 1 4x and g( x) = 6 x, find each of the following. a. ( f + g)() b. ( f g)( ) f c. ( fg)( ) d. (4) g 6. Given f ( x) = ( x ) and g( x) = x + 1, find each of the following. a. ( f g)( ) b. ( g f )( x) 7. Find the inverse of ( ) 5 f x = x. 8. Solve 4x Solve x 1 x = +. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

14 10 Chapter Test Form B 10. The profit from making and selling x units of a product is given by f ( x) = x 1x dollars. How many units should be produced and sold in order to make a profit of $1760? 11. The cost of a birthday party, in dollars, depends on x, the number of people attending the party, and is described below by the piecewise function. 75, x 10 C( x) = ( x 10), x > 10 Find C(1) and interpret its meaning in the context of the problem. 1. The population of a certain city is given in the following table. Year Population 81, , , ,49 95, , ,050 a. Using an input equal to the number of years after 190, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in c. If the population continues according to the model, when will the population of the city drop to 750,000 people again? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

15 1. For each of the following functions, find the value of f ( 4), if possible. 4 a. f ( x) = x 8 x 4, x < b. f ( x) = x + 6, x c. f ( x) = ( x + 5) d. f ( x) = x Find the coordinates of the vertex of the graph for each of the following. a. f ( x) = 5( x + ) + 1 b. f x x x ( ) = Chapter Test Form C 11. The graph of f ( x) ( 4) = x + is shown below. a. Decide whether the function is even, odd, or neither. b. Describe the increasing and decreasing behavior of the function. c. Describe the concavity of the function. d. What is the domain and range of this function? 4. Find the x-intercepts of each function. a. f ( x) = x + 7x 4 b. f x x x ( ) = Given f ( x) = 1 x and g( x) = x +, find each of the following. a. ( f + g)() b. ( f g)( ) f c. ( fg)( ) d. (4) g 6. Given f ( x) = ( x 1) and g( x) = x, find each of the following. a. ( f g)( ) b. ( g f )( x) 7. Find the inverse of f ( x) = 6x Solve x Solve 4x 7 x 1 = +. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

16 1 Chapter Test Form C 10. The profit from making and selling x units of a product is given by f ( x) = x 10x dollars. How many units should be produced and sold in order to make a profit of $700? 11. The cost of gas, in dollars, used by a household in Hennepin County depends on x, the number of therms used each month, and is described below by the piecewise function. 1.5 x, x < 10 C( x) = 1.7 x,10 x < 50. x, x 50 Find C(50) and interpret its meaning in the context of the problem. 1. The population of a certain city is given in the following table. Year Population 600, ,00 700, , , ,765 0,15 a. Using an input equal to the number of years after 190, find a quadratic function to model this data. b. Use the unrounded function to estimate the population in c. If the population continues according to the model, when will the population of the city be 50,000 people? Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

17 Chapter Test Form A 1 1. Use the properties of logarithms to evaluate the expressions. 6 log5 a. log10 b. ln e c. 10 d. ln 0.4 e. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible. 1 a. log ( x 4) b. ln 4x +. Rewrite each expression as a single logarithm. a. ln x ln y b. 1 (ln x + ln y) ln z In Problems 4 8, solve the equation. 4. log5 x = 5. ln x = x = x 8(5 ) = ln(x + 1) = The amount of polonium-1 present at time t is given by A( t) = 70e grams, where t is the time in days that an isotope decays. a. How many grams remain after 100 days? b. How many days will it take for only grams of polonium-1 to remain? 10. The sales for a furniture manufacturer is given in the table below. Year Sales (in millions) a. Find an exponential function that models the data, using an input of the number of years after b. Use the model to estimate furniture sales for Suppose that $4,00 is invested at 6% for 10 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 1. The number of frogs in a lake is given by P( t) = 80e kt, where t = 0 represents the year In 1985 the number of frogs in the lake is 100. a. Find the value of k. b. Use the result from part (a) to predict the number of frogs in Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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19 Chapter Test Form B Use the properties of logarithms to evaluate the expressions. a. log10 b. ln e log6 7 c. 6 d. ln. e. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible. 4 1 a. log(6x + 5) b. ln x. Rewrite each expression as a single logarithm. a. 4 log x ( log y + log z) b. 1 (ln x ln ) In Problems 4 8, solve the equation. 4. log x = 5 5. ln x = x = 1 7. x+ 1 ( ) = ln( x + 1) = h 9. The amount of a drug present in the blood plasma of a patient is given by A( h) = 15e µ g/ml, h hours after the drug reaches its peak concentration. a. What is the concentration of the drug in the blood plasma 8 hours after it reaches peak concentration? b. How many hours after peak concentration will it take for only 10 µ g/ml to remain? 10. The population of a country is given in the table below. Year Population (in millions) a. Find an exponential function that models the data, using an input of the number of years after 190. b. Use the model to estimate the population for Suppose that $6,800 is invested at % for 5 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 1. The number of rabbits in a field is given by P( t) = 15e kt, where t = 0 represents the year In 199 the number of rabbits in the field is. a. Find the value of k. b. Use the result from part (a) to predict the number of rabbits in the field in Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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21 Chapter Test Form C Use the properties of logarithms to evaluate the expressions. 5 log4 a. log10 b. ln e c. 4 d. ln e. Rewrite each expression as the sum, difference, or product of logarithms and simplify if possible. 1 a. log b. ln x(y + 1) y. Rewrite each expression as a single logarithm. a. ln x + 4(ln y ln z) b. 1 (ln x + ln y) ln z In Problems 4 8, solve the equation. 4. log4 x = 5. 1 ln x = 5 6. x+ = x = 10 x 8. ln = 9. A bicyclist begins coasting on flat ground at 0 miles per hour. The cyclist s speed is given by 1.55t v( t) = 0e miles per hour, where t is the number of minutes coasting. a. What is the cyclist s speed after coasting for minutes? b. When is the cyclist s speed 5 miles per hour? 10. The sales for a clothing company are given in the table below. Year Sales (in millions) a. Find an exponential function that models the data, using an input of the number of years after b. Use the model to estimate sales for Suppose that $8600 is invested at 6% for 8 years. Find the total amount present at the end of this time period if the interest is compounded (a) monthly and (b) continuously. 1. The number of turtles in a lake is given by P( t) = 1e kt, where t = 0 represents the year 000. In 005 the number of turtles in the lake is 0. a. Find the value of k. b. Use the result from part (a) to predict the number of frogs in 010. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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23 Chapter 4 Test Form A Consider the function f ( x) = 5x 6x x + 7. a. What is the degree of the polynomial? b. Describe the end behavior of the function.. Graph 1 = using a window that shows a local maximum and local minimum. y x x x a. Where does the local maximum occur? b. Where does the local minimum occur?. Solve 4. Solve x x =. 4 x x 18x = Use factoring by grouping to solve x + x x =. 6. If x = is a solution of = 0, find the remaining solutions. x x x 7. Use the root method to solve ( x 4) = 81. 4x Consider the function y = x 5. a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve x 17x + 16 = Find the exact solutions to = x x + x in the complex number system Solve x. x x + 0.1x 1. The average cost for a certain product is given by C( x) =, where x is the x number of hundreds of units produced. Find the average cost per unit when 000 units are produced. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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25 Chapter 4 Test Form B 1 1. Consider the function f ( x) = x 6x + x 8. a. What is the degree of the polynomial? b. Describe the end behavior of the function.. Graph 1 = 8 + using a window that shows a local maximum and local minimum. y x x x a. Where does the local maximum occur? b. Where does the local minimum occur?. Solve 4. Solve x 9x = 0. 4 x x x = Use factoring by grouping to solve x x + x =. 6. If x = is a solution of = 0, find the remaining solutions. x x x 7. Use the root method to solve ( x + 1) = 16. x Consider the function y =. x a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve x x + =. 10. Find the exact solutions to = x + x + x + in the complex number system Solve x 4 4. x x + 0.1x 1. The average cost for a certain product is given by C( x) =, where x is the number x of hundreds of units produced. Find the average cost per unit when 4000 units are produced. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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27 Chapter 4 Test Form C Consider the function f ( x) = 5x 6x x + 7x. a. What is the degree of the polynomial? b. Describe the end behavior of the function.. Graph y = x + 6x + 1 using a window that shows a local maximum and local minimum. a. Where does the local maximum occur? b. Where does the local minimum occur?. Solve 4. Solve 4 0 x x =. 4 x + 5x 14x = Use factoring by grouping to solve x x + x = If x = 1 is a solution of = 0, find the remaining solutions. x x x 7. Use the root method to solve ( x + 5) = 18. x Consider the function y =. x 4 a. Find the x-intercept and y-intercept of the function. b. Find any horizontal asymptotes that exist. c. Find any vertical asymptotes that exist. 9. Solve x x + =. 10. Find the exact solutions to = in the complex number system. 0 x 7x x Solve x 5 5. x x + 0.1x 1. The average cost for a certain product is given by C( x) =, where x is the x number of hundreds of units produced. Find the average cost per unit when 5000 units are produced. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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29 1. Write the system x + 4y z = 4 x y + 5z = x y z = 1 as an augmented matrix. Chapter 5 Test Form A 5. The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists a b c Solve the system x + y + z = 7 x y + z = 8 x + y z = 7 algebraically, if a solution exists. 4. Solve the system x y + z = 1 x + y z = algebraically, if a solution exists. x y + 4z = 7 5. A theater owner wants to divide a 1500 seat theater into three sections, with tickets costing $10, $0, and $50, depending on the section. He wants to have twice as many $10 tickets as the sum of the other tickets, and he wants to earn $1,000 from a full house. How many of each type of ticket should he sell? 6. Given 1 A = 1, find A Given A = 0 and B = 4, find each of the following, if possible. 7 0 a. A + B b. A B c. AB 8. Given 5 1 A = 0 and 5 1 B = 4, find AB. 9. Show that and are inverses. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

30 6 Chapter 5 Test Form A 10. Given A = 4. 1 a. Find A. b. Use the inverse from part (a) to solve the system of linear equations x + y = 7. x 4y = Youngclaus Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company s trucks can carry 4550 cubic feet and 6,060 pounds, and is insured to carry $5,00, how many units of each product can be carried on the truck? Unit Volume (cubic feet) Weight (pounds) Insurance Value (dollars) Product A Product B Product C Solve the nonlinear system x + y = 4x. x y = 1 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

31 Chapter 5 Test Form B 7 1. Write the system x + y 6z = 5 x y + z = 7 x y 4z = 8 as an augmented matrix.. The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists a b c Solve the system x + y + z = 5 x y + z = 16 x + y z = 9 algebraically, if a solution exists. 4. Solve the system x y + z = 8 x + y z = 11 algebraically, if a solution exists. x y + 4z = A trust account manager has $80,000 to invest in three different accounts. The accounts pay 85, 10%, and 14%, respectively, and the goal is to earn $9,00 with the amount invested at 14% equal to the sum of the other two investments. How much should the account manager invest in each account? 6. Given A 4 = 1, find A Given A = 0 and B = 4, find each of the following, if possible. 7 0 a. A + 4B b. B A c. BA 8. Given 1 1 A = and 0 B = 6, find AB. 9. Show that and are inverses. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

32 8 Chapter 5 Test Form B Given A =. 1 a. Find A. b. Use the inverse from part (a) to solve the system of linear equations 6x + 5y = 9. x + y = Mitchell Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company s trucks can carry 4500 cubic feet and 5,880 pounds, and is insured to carry $5,400, how many units of each product can be carried on the truck? Unit Volume (cubic feet) Weight (pounds) Insurance Value (dollars) Product A Product B Product C Solve the nonlinear system + = x y = 4 x y 5x. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

33 1. Write the system x + 4y z = x 4y + 7z = 6 4x y z = as an augmented matrix. Chapter 5 Test Form C 9. The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists a b c Solve the system x + y + z = 1 x y + z = 1 x + y z = algebraically, if a solution exists. 4. Solve the system x y + z = 1 x + y z = algebraically, if a solution exists. x y + 4z = 5. A theater owner wants to divide a 1800 seat theater into three sections, with tickets costing $10, $0, and $40, depending on the section. He wants to have twice as many $10 tickets as the sum of the other tickets, and he wants to earn $8,000 from a full house. How many of each type of ticket should he sell? 6. Given 4 A = 1 5, find A Given A = 6 5 and B = 4, find each of the following, if possible. 0 a. A + B b. A B c. AB 8. Given 4 1 A = 1 and 1 B = 4, find AB. 9. Show that 7 1 and 7 1 are inverses. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

34 0 Chapter 5 Test Form C Given A = 1. 1 a. Find A. b. Use the inverse from part (a) to solve the system of linear equations 4x + y = 10. x + y = Corey Trucking Company has an order for three product; A, B, and C, for delivery. The following table gives the volume in cubic feet, the weight in pounds, and the value for insurance in dollars for a unit of each of the products. If one of the company s trucks can carry 0 cubic feet and 4,100 pounds, and is insured to carry $19,00, how many units of each product can be carried on the truck? Unit Volume (cubic feet) Weight (pounds) Insurance Value (dollars) Product A Product B Product C Solve the nonlinear system x y = x. 4x + y = 10 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

35 Chapter 6 Test Form A 1 1. Sketch the graph of the inequality x y 4.. Graph the following system of inequalities and identify the corners of the solution region. x + y 8 x + y x + y 4. Graph the solution of the nonlinear inequalities x x + y x + y 10x The corner points of a certain feasibility region are (0, 0), (0, 5), (, ) and (4, 0). Which corner point maximizes the value of C = x + 4y? 5. Find the maximum value of f = 4x + y and the values of x and y that give the value, subject to the constraints x + y 1 x + y 9. x 0, y 0 6. Determine whether each of the following sequences are arithmetic or geometric a.,,,,, b. 8,,, 7, 1, Find the 1 th term of the geometric sequence 6, 1, 4, 48, A ball is dropped from a height of 80 feet and rebounds 5 of the height from which it falls every time it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 50 terms of the arithmetic sequence 0, 5, 40, 45, 50, Find the sum of the geometric series (0.) i. i= Write y = 4 4 x x + x with each term in the form n cx. 1. Find where f '( x ) = 0 if f '( x) (x 1) ( x 6) (x 1) ( x 6) = Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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37 Chapter 6 Test Form B 1. Sketch the graph of the inequality x + y 6.. Graph the following system of inequalities and identify the corners of the solution region. x + y 4 x y 4 y 0. Graph the solution of the nonlinear inequalities 8x x + y 8. ( x 4) 0 y 4. The corner points of a certain feasibility region are (0, 0), (0, 5), (, 4) and (4, 0). Which corner point maximizes the value of C = x + 4y? 5. Find the maximum value of f = x + y and the values of x and y that give the value, subject to the constraints x + y 6 x + y 4. x 0, y 0 6. Determine whether each of the following sequences are arithmetic or geometric. 7 1 a.,,,,, b.,, 4.5,6.75,10.15, Find the 1 th term of the geometric sequence, 6,18, 54, A ball is dropped from a height of 100 feet and rebounds 5 of the height from which it falls every time it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 50 terms of the arithmetic sequence 15, 18, 1, 4, 7, Find the sum of the geometric series. i= 1 5 i Write y = 5 x x + x with each term in the form n cx. 1. Find where f '( x ) = 0 if f '( x) (x 1) ( x ) (x 1) ( x ) 5 4 = Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

38 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

39 Chapter 6 Test Form C 5 1. Sketch the graph of the inequality x y 6.. Graph the following system of inequalities and identify the corners of the solution region. x + 6y 18 x + y 1 x 0, y 0. Graph the solution of the nonlinear inequalities x + x + y y x 8 ( 4) The corner points of a certain feasibility region are (0, 0), (0, 5), (, ) and (4, 0). Which corner point maximizes the value of C = x + y? 5. Find the maximum value of f = 1x + 40y and the values of x and y that give the value, subject to the constraints x + 4y 40 5x + y 16. x 0, y 0 6. Determine whether each of the following sequences are arithmetic or geometric a. 4,,,,, b. 5,, 1, 4, 7, Find the 1 th term of the geometric sequence 6,,,, A ball is dropped from a height of 80 feet and rebounds 4 5 of the height from which it falls every time it hits the ground. How high will the ball bounce after it hits the ground the fourth time? 9. Find the sum of the first 40 terms of the arithmetic sequence 15, 7, 9, 51, 6, Find the sum of the geometric series (0.7) i. i= Write y = 7 6 x x + x with each term in the form n cx. 1. Find where f '( x ) = 0 if f '( x) ( x 4) (x ) ( x 4) (x ) =. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

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41 1. a. Domain = {4,, 1,, 6}, Range = {7, 5,, 0, } b. Domain = {all real numbers}, Range ={ y : y 8 } c. Domain = {all real numbers}, Range = {all real numbers}. a. x-intercept is, y-intercept is -4 b. no x-intercept, y-intercept is c. x-intercepts are 0 and, y-intercept is 0. a. slope = 6, y-intercept is -1 b. slope = 5, y-intercept is -7.5 c. slope = 1, y-intercept is 0 Answers for Chapter 1 Test Form A 7 4. a. -1/ b. 0 c a. 18 members in 1995 b. The y-intercept is 18, which means the initial group membership was 18 members. c. The rate of change is members per year. 6. a. y = x + 4 b. y = x + 19 c. x = 7. a. y = x + 6 b. y = 4x + 8 c. y = 4 8. f ( x + h) f ( x) ( x + h) (x ) h = = = h h h 9. a. The scatterplot appears linear. The first differences range from 6 to 64. b. N( x) = 6.9x books, x years after c thousand books will be checked out in a. (4, ) b. (-1, 4) c. no solution 11. You would need to make and sell 9 wind chimes to break even. 1. The employee needs to sell more than $0,000 in order for the second position to be more profitable. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

42 8 Answers for Chapter 1 Test Form B 1. a. Domain = {-4, -, 1,, 6}, Range = {-1, 1, 4, 7, 9} b. Domain = {all real numbers}, Range ={ y : y 4 } c. Domain = {all real numbers}, Range = {all real numbers}. a. x-intercept is 1, y-intercept is -1 5 b. no x-intercept, y-intercept is - c. x-intercepts are 0 and -, y-intercept is 0. a. slope = 4, y-intercept is 6 b. slope =, y-intercept is c. slope = 0, y-intercept is a. -5/9 b. 4/9 c a grams of the drug is absorbed into the body hours after it is taken b. The y-intercept is 0.4, which means that 0.4 grams of the drug are absorbed initially into the body. c. The rate of change of the absorption of the drug into the body is grams/hour. 6. a. y = x b. y = 4x + 9 c. x = a. y = x + b. y = x + 1 c. y = 4 8. f ( x + h) f ( x) ( x + h) 1 (x 1) h = = = h h h 9. a. The scatterplot appears linear. The first differences range from 0. to 0.4. b. D( x) = 0.06x dollars per share, x years after c. $ 0.70 dividends per share in a. (-, 4) b. (, 10) c. no solution 11. You would need to make and sell bracelets to break even. 1. Torrey needs to score 91 or better to get an A. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

43 1. a. Domain = {-, 0,, 4, 6}, Range = {-, 1, 5, 9, 1} b. Domain = {all real numbers}, Range ={ y : y } c. Domain = {all real numbers}, Range = {all real numbers}. a. x-intercept is 4, y-intercept is -4 b. no x-intercept, y-intercept is 4 c. x-intercepts are 0 and -6, y-intercept is 0. a. slope =, y-intercept is - 5 b. slope =, y-intercept is 5 c. slope =0, y-intercept is 6 4. a. -1/9 b. 0 c. 5 Answers for Chapter 1 Test Form C 9 5. a. 87 books sold 5 weeks after publication b. The y-intercept is, which is the number of books sold during the initial week of publication. c. The rate of change in the number of books sold is 51 books per week. 6. a. y = x + 5 b. y = x + c. x = a. y = x + b. y = x + 1 c. y = 8. f ( x + h) f ( x) 4( x + h) + (4x + ) 4h = = = 4 h h h 9. a. The scatterplot appears linear. The first differences range from 0.4 to 0.5. b. D( x) = 0.045x dollars per share, x years after c. $ 0.96 dividends per share in a. (, -6) b. (-1, ) c. no solution 11. You would need to make and sell 7 cutting boards to break even. 1. Kenny needs to score 8 or better to get a B. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

44 40 Answers for Chapter Test Form A 1. a. 6 b. 8 c. 9 d. 7. a. (5, 1) b. (-, -). a. neither b. decreasing for x < 1, increasing for x > 1 c. concave up d. Domain = {all real numbers}, Range = { y : y } 4. a. (-, 0) and (5, 0) b. (0.178, 0) and (.8, 0) 5. a. 9 b. 5 c. 4 d a b. ( g f )( x) = ( x + 1) 7. ( ) = 4 f x x 8. x x = units 11. The cost of a movie ticket for a person who is 5 years old is $7. 1. a. P( t) = t +, 09.9t + 797, people, t years after 190 b. 898,5 people c. early 1984 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

45 Answers for Chapter Test Form B a. 1 b. 11 c. 18 d. 4. a. (-4, -) b. (, ). a. even b. increasing for x < 0, decreasing for x > 0 c. concave down d. Domain = {all real numbers}, Range = { y : y 8} 4. a. (7, 0) and (, 0) b. (-1.816, 0) and (-0.184, 0) 5. a. -17 b. -68 c. -10 d a. 9 b. ( g f )( x) = ( x ) ( ) = + 5 f x x 7 5 x x = 5, units 11. The cost of a birthday party with 1 people will be $ a. P( t) = 95.91t + 6, t + 68, people, t years after 190 b. 917,5 people c. middle of 1989 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

46 4 Answers for Chapter Test Form C 1. a. - 1/ b. -1 c. -1 d. 16. a. (-, 1) b. (-.5,-4.5). a. neither b. decreasing for x < 4, increasing for x > 4 c. concave up d. Domain = {all real numbers}, Range = { y : y 0} 4. a. (-1/, 0) and (4, 0) b. (0.17, 0) and (5.88, 0) 5. a. -1 b. -1 c. 66 d a. 7 1 b. ( g f )( x) = ( x 1) f ( x) = x x 9. x = units 11. The cost of gas for a family that uses 50 therms in a month is $ a. P( t) = 8.7t + 8, t + 60, people, t years after 190 b. 6,551 people c. early 198 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

47 Answers for Chapter Test Form A 4 1. a. 6 b. c. 5 d a. log( x + 4) b. 1 ln(4x ). a. b. ln x y ( ) ln xy z 4. x = x = 5 ln10 + ln 6 x = = 4.85 ln 6 ln(1.5) x = = ln ( 9 1) x = e = 9. a grams b. 718 days 10. a. S( t ) =.98(1.17) t millions, t years after 1974 b million 11. a. $ b. $ ln(1.5) 1. a. k = 5 b. 15 frogs Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

48 44 Answers for Chapter Test Form B 1. a. b. - c. 7 d... a. 4 log(6x + 5) b. 1 ln x. a. 4 log x y z b. ln x 4. x = e x = ln1 x = = 0.69 ln 6 ln 5 ln x = = ln 4 ( 1) x = e = 9. a µ g / ml b hours 10. a. P( t ) = 1.588(1.07) t millions, t years after 190 b million people 11. a. $14,8.1 b. $14, a. k = ln 15 b. 48 rabbits Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

49 Answers for Chapter Test Form C a. 5 b. 1/ c. d a. log y b. ln x + ln(y + 1). a. b. 4 y ln x z ln xy z 4. x = x = e 10 ln 4 ln x = = 1 ln ln10 x = = ln x = e = 9. a miles/ hour b minutes 10. a. S( t ) = 8(1.65) t millions, t years after 1974 b million 11. a. $1,881.6 b. $1,898.4 ln(.5) 1. a. k = 5 b. 95 turtles Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

50 46 Answers for Chapter 4 Test Form A 1. a. 4 th degree b. both ends open up. a. local maximum at (-, -1) b. local minimum at (-1, - 1/). x = 0,, 4. x = 0,, x =, 5, x = 5, 4 7. x = 7 8. a. x-intercept (-1/4, 0) and y-intercept (0, -1/5) b. y = 4 c. x = 5 9. x = 1,1, 4, x = 4, i, i 11. x > 8 1. average cost per unit is 56. Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

51 Answers for Chapter 4 Test Form B a. rd degree b. opens down on right 1. a. local maximum at (, 11 ) b. local minimum at (4, 4 ). x = 0,, 4. 1 x = 0,, 5. x =, 5 i, 5 i 6. x = 6, 1 7. x = 1 8. a. x-intercept (-, 0) and y-intercept (0, ) b. y = c. x = x =,,, x =, + i, i x > 1. average cost per unit is 4 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

52 48 Answers for Chapter 4 Test Form C 1. a. 6 th degree b. both ends open down. a. local maximum at (-, 9) b. local minimum at (0, 1). x = 0, 1,1 4. x = 0, 7, 5. x = 4, i, i 6. x = 4, 7. x = 1 8. a. x-intercept (-4, 0) and y-intercept (0, -) b. y = c. x = x =,,, x = 4, + i, i x > average cost per unit is 5 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

53 Answers for Chapter 5 Test Form A a. (6, -, 5) b. (6, 4, ) c. (-a + 6, -a, a). (1, -, 4) 4. no solution $10 tickets, 500 $0 tickets, 50 $50 tickets a b c. impossible = a. 4 b. (5, 1) units of Product A, 60 units of Product B, 50 units of Product C 1. (1, ) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

54 50 Answers for Chapter 5 Test Form B a. (8,, -) b. (6, -, ) c. no solution. (6, 1, -1) 4. no solution 5. $0,000 at 8%, $0,000 at 10%, $40,000 at 14% a b c. impossible = a b. (-1, ) units of Product A, 80 units of Product B, 40 units of Product C 1. (4, 4) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

55 Answers for Chapter 5 Test Form C a. (5, -1, -6) b. (6,, ) c. no solution. (-,, ) 4. (0.5a + 0.5,.5a + 1.5, a) $10 tickets, 400 $0 tickets, 00 $50 tickets a b c. impossible = a b. (, -) units of Product A, 40 units of Product B, 0 units of Product C 1. (, ) Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

56 5 Answers for Chapter 6 Test Form A (0, 4), (4, ), (, 0) corner points (, 16) and (5, 5) 4. (0, 5) 5. (, 6) f = 0 6. a. geometric b. arithmetic 7. -1, feet y = x x + 4x 1 5 x =,6, 4 1/ 4 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

57 Answers for Chapter 6 Test Form B (0, 4), (-, 0), (4, 0) corner points (, 16) and (6, 16) 4. (, 4) 5. (, ) f = a. arithmetic b. geometric , feet y = x x + 5x 5 1/ 1 1 x =,, 4 Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.

58 Answers for Chapter 6 Test Form C (6, 0), (, /), (18, 0). corner points (0, 8) and (, -7) 4. (, ) 5. (0, 0) f = a. geometric b. arithmetic feet y = x x + 4x x = 1, 4, 7 6 / Copyright 007 Pearson Education, publishing as Pearson Addison-Wesley.