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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042
BuyFind

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042

Solutions

Chapter
Section
Chapter 5.1, Problem 28E
Textbook Problem

For Problems 31 and 32, let f ( x ) =  c ( l   + e a x ) with a > 0. Use a graphing utility to graph the functions.

(a) Fix c = 50 and graph y = f ( x )   =   50 (   1   + e a x ) for a = 0.1,1, and 10.

(b) What effect does a have on the graphs?

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Chapter 5 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
Ch. 5.1 - In Problems 9-20, graph each function. 9. Ch. 5.1 - In Problems 9-20, graph each function. 10. Ch. 5.1 - In Problems 9-20, graph each function. 11. Ch. 5.1 - In Problems 9-20, graph each function. 12. Ch. 5.1 - In Problems 9-20, graph each function. 13. Ch. 5.1 - In Problems 9-20, graph each function. 14. Ch. 5.1 - In Problems 9-20, graph each function. 15. Ch. 5.1 - In Problems 9-20, graph each function. 16. Ch. 5.1 - In Problems 9-20, graph each function. 17. Ch. 5.1 - In Problems 9-20, graph each function. 18. Ch. 5.1 - In Problems 9-20, graph each function. 19. Ch. 5.1 - In Problems 9-20, graph each function. 20. Ch. 5.1 - 21. (a) Find a > 1 to express in the form . (b)...Ch. 5.1 - 22. (a) Find a > 1 to express in the form . (b)...Ch. 5.1 - 23. (a) Graph . (b) Graph . (c) Algebraically show...Ch. 5.1 - 24. (a) Graph . (b) Graph . (c) Algebraically show...Ch. 5.1 - 25. Given that , write an equivalent equation in...Ch. 5.1 - 26. Given that , write an equivalent equation in...Ch. 5.1 - In Problems 27-30, use a graphing utility to...Ch. 5.1 - In Problems 27-30, use a graphing utility to graph...Ch. 5.1 - In Problems 27-30, use a graphing utility to...Ch. 5.1 - In Problems 27-30, use a graphing utility to...Ch. 5.1 - For Problems 31 and 32, let with a > 0. Use a...Ch. 5.1 - For Problems 31 and 32, let with a > 0. Use a...Ch. 5.1 - 33. Compound interest If $1000 is invested for x...Ch. 5.1 - 35. Compound interest We will show in the next...Ch. 5.1 - 36. Compound interest If $1000 is invested for x...Ch. 5.1 - 37. Drug in the bloodstream The percent...Ch. 5.1 - Bacterial growth A single bacterium splits into...Ch. 5.1 - 39. Product reliability A statistical study shows...Ch. 5.1 - Population growth Use the following information...Ch. 5.1 - Population growth Use the following information...Ch. 5.1 - Population growth Use the following information to...Ch. 5.1 - 46. Advertising and sales Suppose that sales are...Ch. 5.1 - 47. Modeling Carbon dioxide emissions The...Ch. 5.1 - 53. Modeling Alzheimer’s disease As the baby...Ch. 5.2 - 1. What asymptote does the graph of approach when...Ch. 5.2 - 2. For , does the equation represent the same...Ch. 5.2 - 3. For what values of , defined? Ch. 5.2 - 4. (a) Write in exponential form and find x. (b)...Ch. 5.2 - 5. Simplify: (a) (b) (c) (d) log 1 Ch. 5.2 - 6. If and , find the following. (a) (b) (c) Ch. 5.2 - In Problems 1-4, use the definition of a...Ch. 5.2 - In Problems 1-4, use the definition of a...Ch. 5.2 - In Problems 1-4, use the definition of a...Ch. 5.2 - In Problems 1-4, use the definition of a...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 5-14, solve for x by writing the...Ch. 5.2 - In Problems 15-18, write the equation in...Ch. 5.2 - In Problems 15-18, write the equation in...Ch. 5.2 - In Problems 15-18, write the equation in...Ch. 5.2 - In Problems 15-18, write the equation in...Ch. 5.2 - In Problems 19 and 20, write the equation in...Ch. 5.2 - In Problems 19 and 20, write the equation in...Ch. 5.2 - In Problems 21-26, graph each function. 21. Ch. 5.2 - In Problems 21-26, graph each function. 22. Ch. 5.2 - In Problems 21-26, graph each function. 23. Ch. 5.2 - In Problems 21-26, graph each function. 24. Ch. 5.2 - In Problems 21-26, graph each function. 25. Ch. 5.2 - In Problems 21-26, graph each function. 26. Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 27 and 28, use properties of...Ch. 5.2 - In Problems 35 and 36, evaluate each logarithm...Ch. 5.2 - In Problems 35 and 36, evaluate each logarithm...Ch. 5.2 - Write each expression in Problems 37-40 as the sum...Ch. 5.2 - Write each expression in Problems 37-40 as the sum...Ch. 5.2 - Write each expression in Problems 37-40 as the sum...Ch. 5.2 - Write each expression in Problems 37-40 as the sum...Ch. 5.2 - Use the properties of logarithms to write each...Ch. 5.2 - Use the properties of logarithms to write each...Ch. 5.2 - Use the properties of logarithms to write each...Ch. 5.2 - Use the properties of logarithms to write each...Ch. 5.2 - In Problems 45-48, use a calculator to determine...Ch. 5.2 - In Problems 45-48, use a calculator to determine...Ch. 5.2 - In Problems 45-48, use a calculator to determine...Ch. 5.2 - In Problems 45-48, use a calculator to determine...Ch. 5.2 - 49. (a) Use a graphing utility to graph = In x and...Ch. 5.2 - 50. Use a graphing utility to graph = In x and =...Ch. 5.2 - In Problems 51 and 52, use a change-of-base...Ch. 5.2 - In Problems 51 and 52, use a change-of-base...Ch. 5.2 - In Problems 53-56, use a change-of-base formula...Ch. 5.2 - In Problems 53-56, use a change-of-base formula...Ch. 5.2 - In Problems 53-56, use a change-of-base formula...Ch. 5.2 - In Problems 53-56, use a change-of-base formula...Ch. 5.2 - 57. Prove logarithmic Property IV. Ch. 5.2 - 58. Prove logarithmic Property V. Ch. 5.2 - Richter scale Use the formula in Problems 59-62....Ch. 5.2 - Richter scale Use the formula in Problems 59-62....Ch. 5.2 - Richter scale Use the formula in Problems 59-62....Ch. 5.2 - Richter scale Use the formula in Problems 59-62....Ch. 5.2 - Decibel readings In Problems 63-66, use the fact...Ch. 5.2 - Decibel readings In Problems 63-66, use the fact...Ch. 5.2 - Decibel readings In Problems 63-66, use the fact...Ch. 5.2 - pH levels In Problems 67-70, use the following...Ch. 5.2 - pH levels In Problems 67-70, use the following...Ch. 5.2 - pH levels In Problems 67-70, use the following...Ch. 5.2 - pH levels In Problems 67-70, use the following...Ch. 5.2 - Doubling time In Problems 71 and 72, use the...Ch. 5.2 - Doubling time In Problems 71 and 72, use the...Ch. 5.2 - 73. Women in the workforce For selected years from...Ch. 5.2 - 75. Modeling Diabetes As the following table...Ch. 5.2 - 76. Modeling Female workers The percent of all...Ch. 5.2 - 78. Modeling Demographics The table below gives...Ch. 5.3 - 1. Suppose the sales of a product, in dollars, are...Ch. 5.3 - 2. Suppose the monthly demand for a product is...Ch. 5.3 - 3. Suppose the number of employees at a new...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - In Problems 1-22, solve each equation. Give...Ch. 5.3 - For Problems 23 and 24, let Use a graphing...Ch. 5.3 - For Problems 23 and 24, let Use a graphing...Ch. 5.3 - 25. Sales decay The sales decay for a product is...Ch. 5.3 - 26. Sales decay The sales of a product decline...Ch. 5.3 - 27. Inflation The purchasing power P (in dollars)...Ch. 5.3 - 28. Product reliability A statistical study shows...Ch. 5.3 - 29. Radioactive half-life An initial amount of 100...Ch. 5.3 - 30. Radioactive half-life A breeder reactor...Ch. 5.3 - 31. Population growth If the population of a...Ch. 5.3 - 32. Population growth The population of a certain...Ch. 5.3 - 35. Demand The demand function for a certain...Ch. 5.3 - 36. Demand The demand function for a product is...Ch. 5.3 - 37. Supply If the supply function for a product is...Ch. 5.3 - 38. Supply If the supply function for a product is...Ch. 5.3 - 39. Total cost The total cost function for x units...Ch. 5.3 - 40. Total cost The total cost function for a...Ch. 5.3 - 41. Demographics The millions of White...Ch. 5.3 - 42. Diabetes Centers for Disease Control and...Ch. 5.3 - 43. Compound interest If $8500 is invested at...Ch. 5.3 - 44. Compound interest If $1000 is invested at 10%...Ch. 5.3 - 45. Compound interest If $5000 is invested at 9%...Ch. 5.3 - 46. Compound interest If $10,000 is invested at 1%...Ch. 5.3 - Profits An investment services company experienced...Ch. 5.3 - Profits An investment services company experienced...Ch. 5.3 - 49. Purchasing power Using Social Security...Ch. 5.3 - 50. China's shale-natural gas The function that...Ch. 5.3 - 51. Supply Suppose the supply of x units of a...Ch. 5.3 - 52. Demand Assume that the demand function for a...Ch. 5.3 - 53. Sales growth The president of a company...Ch. 5.3 - 54. Organizational growth Because of a new market...Ch. 5.3 - 55. Organizational growth Suppose that the...Ch. 5.3 - 56. Sales growth A firm predicts that sales will...Ch. 5.3 - 57. Drugs in the bloodstream The concentration y...Ch. 5.3 - 58. Population growth Suppose that the number y of...Ch. 5.3 - 59. Spread of disease On a college campus of...Ch. 5.3 - 60. Spread of a rumor The number of people N(t) in...Ch. 5.3 - 61. Market share Suppose that the market share y...Ch. 5.3 - 62. Advertising An advertising agency has found...Ch. 5.3 - 63. Pollution Pollution levels in a lake have been...Ch. 5.3 - 64. Fish length Suppose that the length x (in...Ch. 5.3 - 65. U.S. civilian labor force Using U.S. Bureau of...Ch. 5.3 - 66. Chemical reaction When two chemicals, A and B,...Ch. 5.3 - 67. Modeling Diabetes The following table gives...Ch. 5 - 1. Write each statement in logarithmic form. Ch. 5 - 2. Write each statement in exponential form. Ch. 5 - Graph the following functions. 3. Ch. 5 - Graph the following functions. 4. Ch. 5 - Graph the following functions. 5. Ch. 5 - Graph the following functions. 6. Ch. 5 - Graph the following functions. 7. Ch. 5 - Graph the following functions. 8. Ch. 5 - Graph the following functions. 9. Ch. 5 - Graph the following functions. 10. Ch. 5 - Graph the following functions. 11. Ch. 5 - Graph the following functions. 12. Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 13-20, evaluate each logarithm without...Ch. 5 - In Problems 21-24, if , find each of the following...Ch. 5 - In Problems 21-24, if , find each of the following...Ch. 5 - In Problems 21-24, if , find each of the following...Ch. 5 - In Problems 21-24, if , find each of the following...Ch. 5 - In Problems 25 and 26, use the properties of...Ch. 5 - In Problems 25 and 26, use the properties of...Ch. 5 - 27. Is it true that ln for all positive values of...Ch. 5 - 28. If Ch. 5 - 29. If Ch. 5 - 30. If Ch. 5 - 31. If Ch. 5 - In Problems 32 and 33, use a change-of-base...Ch. 5 - In Problems 32 and 33, use a change-of-base...Ch. 5 - In Problems 34 and 35, rewrite each logarithm...Ch. 5 - In Problems 34 and 35, rewrite each logarithm...Ch. 5 - In Problems 36-42, solve each equation. 36. Ch. 5 - In Problems 36-42, solve each equation. 37. Ch. 5 - In Problems 36-42, solve each equation. 38. Ch. 5 - In Problems 36-42, solve each equation. 39. Ch. 5 - In Problems 36-42, solve each equation. 40. Ch. 5 - In Problems 36-42, solve each equation. 41. Ch. 5 - In Problems 36-42, solve each equation. 42. Ch. 5 - 43. Medicare spending The graph in the following...Ch. 5 - 45. Inflation The purchasing power P of a $60,000...Ch. 5 - 46. Modeling Average annual wage The following...Ch. 5 - 48. Modeling U.S. population The following table...Ch. 5 - 49. Stellar magnitude The stellar magnitude M of a...Ch. 5 - 50. Sales decay The sales decay for a product is...Ch. 5 - 53. Sales decay The sales decay for a product is...Ch. 5 - 54. Compound interest If $1000 is invested at 12%,...Ch. 5 - 55. Compound interest If $5000 is invested at...Ch. 5 - 56. World population With data from the...Ch. 5 - Advertising and sales Because of a new advertising...Ch. 5 - 58. Spread of a disease The spread of a highly...Ch. 5 - In Problems 1-4, graph the functions. 1. Ch. 5 - In Problems 1-4, graph the functions. 2. Ch. 5 - In Problems 1-4, graph the functions. 3. Ch. 5 - In Problems 1-4, graph the functions. 4. Ch. 5 - In Problems 5-8, use technology to graph the...Ch. 5 - In Problems 5-8, use technology to graph the...Ch. 5 - In Problems 5-8, use technology to graph the...Ch. 5 - In Problems 5-8, use technology to graph the...Ch. 5 - In Problems 9-12, use a calculator to give a...Ch. 5 - In Problems 9-12, use a calculator to give a...Ch. 5 - In Problems 9-12, use a calculator to give a...Ch. 5 - In Problems 9-12, use a calculator to give a...Ch. 5 - 13. Use the definition of a logarithmic function...Ch. 5 - 14. Write in logarithmic form. Ch. 5 - In Problems 15 and 16, solve each equation for x...Ch. 5 - In Problems 15 and 16, solve each equation for x...Ch. 5 - In Problems 17-20, simplify the expressions using...Ch. 5 - In Problems 17-20, simplify the expressions using...Ch. 5 - In Problems 17-20, simplify the expressions using...Ch. 5 - In Problems 17-20, simplify the expressions using...Ch. 5 - 21. Write ln as a sum involving M and N. Ch. 5 - 22. Write as a difference involving two...Ch. 5 - 23. Write as a base e logarithm using a...Ch. 5 - 24. Solve for Ch. 5 - 25. The graph in the following figure shows the...Ch. 5 - 26. With data from the U.S. Energy Information...Ch. 5 - 27. The total national health expenditures per...Ch. 5 - 28. A company plans to phase out one model of its...Ch. 5 - 31. Modeling The following table gives the...

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