Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Mathematical Applications for the Management, Life, and Social Sciences
APPLICATIONS Annuity The formula for the future value of an annuity due involves the expression (1+i)n+11i1 Write this expression over a common denominator and factor the numerator to simplify.Solve the equations in Problems 1-6
Solve the equations in problem 1-6.
2.
3RE4RE5RESolve the equations in problems 1-6
6.
7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17REIn Problem 18 and 19, determine whether each graph represents as a function of .
19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33REIn problems 31-38, write the equation of each line described.
34. Through and
35RE36RE37RE38RE39RE40RE41RE42RE43RE44REIn Problem 45-51, solve each system of equations.
45.
46RE47RE48RE49RE50RE51RE52. Life expectancy at age 65 Using Social security Administration data for selected years from 1950 and projected to 2050, the additional years of life expectancy at age 65 can be modified by
where equals the number of years past 1950.
To what year does correspond?
What is the predicted additional years of life expectancy of a 65-years old in 2050?
In what year does the function predict the life expectancy to be 20 years after age 65?
53. Course grades In a certain course, grades are based on three tests worth 100 points each, three quizzes worth 50 points each, and a final exam, worth 200 points. A student has test grades of 91, 82, and 88 and quiz grades of 50, 42, and 42. What is the lowest percent the student can get on the final and still earn an A (90% or more of the points) in the course?
54. Cost analysis The owner of a small construction business needs a new truck. He can buy a diesel truck for $58,000, and it will cost him $0.76 per mile to operate. He can buy a gas engine truck for $53,200, and it will cost him $0.88 per mile to operate. Find the number of miles he must drive before the costs are equal. If he normally keeps a truck for 7 years, which is the better buy?
55RE56RE57RE58. Fish species growth For many species of fish, the weight is a function of the length that can be expressed by
Suppose that for a particular species, and that for this species, the length (in centimeters) is a function of the number of years the fish has been alive and that this function is given by
Find to express as a function of the age of the fish.
59RE60RE61RE62RE63RE64RE65.Flow rates of water -The speed at which water travels in
A pipe can be measured by directing the flow through an
Elbow and measuring the height to which it spurts out
The top. If the elbow height is 10cm,the equation relating
The height h (in centimeters )of the water above the elbw
And its velocity v(in centimeters per second )is given by
(a)Solve the equation for h and graph the result,
Using the velocity as the independent variable.
(b)If the velocity is 210 cm/sec, what is the height
Of the water above the elbow?
66. Investment mix āA retired couple have $600,000 to
Invest and want to earn $60,000 per year in interest.
The safer investment yields 9.5%,but they can supplement
Their earnings by investing some of their money at 11%.How
Much should they invest at each rate to earn $60,000 per year?
67.Botany A botanist has a 20% solution and a 70%
Solution of an insecticide. How much of each must be used
To make 4.0 liters of a 35% solution?
68RE69RE70RECost, revenue and profit A certain commodity sells for $52 per unit and has the following costs for a period.
Fixed cost: $1500
Variable cost per unit: $22
What is the total cost function?
What is the total revenue function?
What is the profit function?
What is the marginal cost?
What is the marginal revenue?
What is the marginal profit?
What is the break-even quantity?
72. Market analysis āThe supply function and the demand
Function for a product are linear and are determined by
The tables that follow.
(a)Write an equation for the supply function and an
Equation for the demand function.
(b)Find the quantity and price that give market
Equilibrium.
73. Market analysis Suppose that for a certain product, the
Supply and demand functions prior to any taxation are
Supply :
Demand :
If a tax of $2 per item is levied on the supplier and is
Passed on to the consumer as a price increase ,find the
Market equilibrium after the tax is levied.
1T2T3T4T5T6T7T8T9T10T11T12T13T14T15T16T[Type here]
Using U.S. Bureau of Labor Statistics data for selected years from and projected to, the number of men in the U.S. workforce (in millions) can be approximated by
where equals the number of years past 1950.
Use a graphing calculator to graph this equation with the window
The point lies on the graph of this equation. Explain its meaning.
Find the projected number of men in the U.S. workforce in according to this model.
[Type here]
18TThe selling price for each item of a product is $50, and The total cost is given by C(x)=10x+18000, where x is the number Of items. Write the revenue functions. Find C(100) and write a sentence that explain its Meaning. (C) Find the number of units that gives the break-even Point.The supply function for a product is p=5q+1500, And the demand function is p=3q+3100. Find the quantity And price that give market equilibrium.21TAn airline has 360 seats on a plane for one of its flights. If 90 of the people making reservations actually buy a ticket, How many reservations should the airline accept to be confident that It will sell 360 tickets?Amanda plans to invest $20,000, part of it at a 9 Interest rate and part of it in a safer fund that pays 6. How much should be invested in each fund to yield an annual Return of $1560?I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
1. Write the functions for the hospital's total cost, total revenue, and profit as functions of the number of surgery cases.
I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
2. How many laser eye operations must the hospital perform each year to break even?
I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
3. Southwest Hospital currently averages 70 laser eye operations per month. One of the nurses has just learned about a machine that would reduce by 5100 per patient the amount of medical supplies needed. It can be leased for 5100.000 annually. Keeping in mind the financial cost and benefits, advise the hospital on whether it should lease this machine.
I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
4. An advertising agency has proposed to the hospitals president that she spend $20.000 per month on television and radio advertising to persuade people that Southwest Hospital is the best place to have laser eye surgery performed. Advertising account executives estimate that such publicity would increase business by 40 operations per month. If they are correct and if this increase is not big enough to affect fixed costs, what impact would this advertising have on the hospitals profits?
I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
5. In case the advertising agency is being overly optimistic, how many extra operations per month are needed to cover the cost of the proposed ads?
I. Hospital Administration
Southwest Hospital has an operating room used only for laser eye surgery. The annual cost of rent, heat and electricity for the operating room and its equipment is $1.08 million, and the annual salaries of the people who staff this room total $1.6 million.
The cost for each surgery is $2395, which includes all medical supplies and drugs and a complimentary bouquet of flowers for each patient. In addition, one-quarter of the patients require dark glasses that the hospital provides at no additional charge but cost $20 per pair. The hospital receives a payment of 56000 for each eye operation performed.
6 If the ad campaign is approved and subsequently meets its projections, should the hospital review its decision about the machine discussed in Question 3?
1EAGP22EAGP23EAGP24EAGP21. Solve the following for x.
(a)
(b)
(c)
2. Solve for y:
3CP4CP5CP
In problems 1-16, solve each equation.
Solve
2E3E4EIn problems 1-16, solve each equation.
5. Solve
6E7E8EIn problems 1-16, solve each equation.
9. Solve
10E11E12E13EIn problems 1-16, solve each equation.
14.
15E16E17E18E19E20E21E22E23E24E25EIn Problems 23 ā 26, use a calculator to solve each equation. Round your answer to three decimal places.
26.
27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45. Depreciation A $648,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by dollars. After how many months will the value of the building be $387,000?
46. Depreciation When an $810,000 building is depreciated for tax purposes (by the straight-line method), its value y, after x months of use is given by
. How many months will it be before the building is fully depreciated (that is, its value is $0)? How many years is this?
47. Credit card debt High interest rates make it difficult for people to pay off credit card debt in a reasonable period of time. The interest I (in dollars) paid on a $10,000 debt over 3 years when the interest rate is r% can be approximated by the equation
If the credit card interest rate is 19.8%, find the amount of interest paid during the 3 years.
48. Seawater pressure In seawater, the pressure p is related to the depth d according to
Where d is in feet and p is in pounds per square inch.
Solve this equation for p in terms of d.
The Titanic was discovered at a depth of 12,460 ft. Find the pressure at this depth.
49. Break-even Burnem Inc. manufactures thumb drives and sells them to a distributor. Burnemās total cost and total revenue (in dollars) for x thumb drives are given by
Total Cost = 2x + 7920 and Total Revenue = 20x
How many thumb drives must Burnem sell to break even?
50. Break-even Dish systems manufactures satellite systems and has its monthly profit P in dollars related to the number of satellite systems, x, by
Find the number of systems that Dish systems need to produce and sell to break even?
51. Profit In its second year of operation, a local Internet providerās profits were $175,000. If this amount was 576% of the companyās first-year profits, find the first-year profits (to the nearest hundred dollars).
52. Sales Tax The total price of a used car (including 6% sales tax) is $21,041. How much of this is tax?
53. United Kingdom Population Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation
Where x is the number of years after 2000
What is the projected population in 2024?
In what year is the population predicted to be 67.2 million?
54. Out-of-Pocket health care expenses Data and projections from the Centres for Medicare and Medicaid Services from 2010 to 2014 indicate that the annual per capita out-of-pocket expenses for healthcare can be approximated by
Where x is the number of years past 2000. When are the per capita out-of-pocket expenses for healthcare predicted to be $1400?
55. Course grades To earn an A in a course, a student must get at least a 90 average on four tests and a final exam, with the final exam weighted twice that of any one test. If the four test scores are 93, 69, 89, and 97, what is the lowest score the student can earn on the final exam and still get an A in the course?
56. Course grades Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she also will change the lowest test score to match the final exam score if the final exam score is higher. If a studentās four test scores are 83, 67, 52, and 90, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course?
57. Investment mix A retired woman has $120,000 to invest. She has chosen ne relatively safe investment fund that has an annual yield of 9% and another risker fund that has a 13% annual yield. How much she invest in each fund if she would like to earn $12,000 per year from her investments?
58. Investment yields One safe investment pays 10% per year, and a riskier investment pays 18% per year. A woman who has $145,600 to invest wants to have an income of $20,000 per year from her investments. How much should she invest at each rate?
59. Salary increases A woman making $2000 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. Find her salary after the raise. What percent change is this from the $2000 per month?
60. Wildlife management In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used:
If in the second capture of 100, it is found that 3 are marked, what is the population?
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000, it is found that 63 are marked. What is the population estimate?
61. Profit For a certain product, the revenue is given by and the cost is given by . To obtain a profit, the revenue must be greater than the cost. For what values of x will there be profit? Graph the solution.
62. Car Rental Thrift rents a compact car for $33 a day, and General rents a similar car for $20 per day plus an initial fee of $78. For how many days would it be cheaper to rent from General? Graph the solution.
63. Purchasing Sean can spend at most $900 for a camera and some memory sticks. He plans to buy the camera for $695 and sticks for $5.75 each. Write an inequality that could be used to find the numbers (x) that he could buy. How many sticks could he buy?
64. Taxes In Sweetwater, Arizona, water bills are taxed in the basis of the amount of the monthly bill to encourage conservation. If the bill is more than $0 but less than $60, the tax is 2% of the bill; If the bill is $60 or more but less than $80, the tax is 4% of the bill; and if the bill is $80 or more, the tax is 6% of the bill. Write the inequalities that represent the amounts of tax owed in these three cases.
65E66. Disposable income per capita Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy information administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation
I = 707.6t + 39,090
Where t is the number of years after 2015.
What t-value corresponds to 2023?
Find the predicted U.S. per capita real disposable income (to the nearest
$10) in 2023.
In what year is the U.S. per capita real disposable income expected to exceed $55,000?
67E68. Wind chill The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to
WC = 1.337t ā 24.094
For what temperatures does it feel at least 30Ā°F colder than the air temperature? That is, find t such that WC ā¤ t ā 30.
1. If y = f(x), the independent variable is ________ and the dependent variable is _________.
2CP3CP4CP5CP6CP1E2EIn Problems 3 and 4, are the relations defined by the tables functions of x? Explain why or why not and give the domain and range.
3.
x 1 2 3 8 9
y -4 -4 5 16 5
4E5E6E7E8E9. If , find the following.
(a) (b) (c) (d)
10. If , find the following.
(a) (b) (c) (d)
11. If , find the following.
(a) (b) (c) (d)
12. If , find the following.
(a) (b) (c) (d)
13. If , find the following.
(a) (b) (c) (d)
14. If , find the following.
(a) (b) (c) (d)
15. If , find the following.
(a) (b) (c)
16. If , find the following.
(a) (b) (c)
17E18. Let and .
Does ?
Find .
Does
Does
Find and simplify
19E20. If and , find the following and simplify.
(a) (b)
21E22. Suppose y = g(x) has the graph in Problem 6(b).
(a) Find g(0).
(b) How many x-values in the domain of this function satisfy g(x) = 0?
23E24E25EState the domain and range of each of the function in Problems 25 ā 28.
26. .
27E28EIn Problems 29 ā 32, a function and its graph are given. In each problem, find the domain.
29.
30E31E32E33EFor and given in the Problems 33 ā 36, find
(a)
(b)
(c)
(d)
34.
35E36EFor and given in the Problem 37 ā 40, find
(a)
(b)
(c)
(d)
37.
For and given in the Problem 37 ā 40, find
(a)
(b)
(c)
(d)
38.
For and given in the Problem 37 ā 40, find
(a)
(b)
(c)
(d)
39.
40E41. Mortgage A couple seeking to buy a home decides a monthly payment of $1600 fits their budget. The amount they can borrow, A, is a function of t, in years, it will take to repay the debt. If we denote this function by A = f(t), then the following table defines the function.
t A t A
5 80,000 20 199,000
10 135,000 25 217,000
15 173,000 30 229,000
Find f(20) and write a sentence that explains its meaning.
Does f(5 + 5) = f(5) + f(5)? Explain.
If the couple is looking at a house that requires them to finance $173,000, how long must they make payments? Write this correspondence in the form A = f(t).
42. Debt refinancing When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7% and a coupleās current debt $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan, t, in years. If we represent this function R = f(t), then the following tables defines the function.
t A t A
5 1980.12 15 898.83
10 1161.09 20 775.3
15 1028.39 25 706.78
If the couple refinances for 20 years, what is the monthly payment? Write this correspondence in the form R = f(t).
Find f(10) and write a sentence that explains its meaning.
Does f(5 + 5) = f(5) + f(5)? Explain.
43E44. Dow Jones Industrial Average The graph shows the Dow Jones Industrial Average on a particularly tumultuous day soon after the U.S. credit rating was downgraded from AAA to AA+ in 2011. If t represents the number of hours after 9:30 a.m., then the graph defines the Dow Jones Industrial Average D as a function of time t. If we represent this function by D = f(t), use the graph to complete the following
Find f(0) and f(6.5).
Find the domain and range for D = f(t) as defined by the graph.
About how many t-values satisfy f(t) = 11,000? Estimate one such t-value.
45E46E47. Temperature measurement The equation
gives the relation between temperature readings in Celsius and Fahrenheit.
Is C a function of F?
What is the mathematical domain of this function?
If we consider this equation as relating temperatures of water in its liquid state, what are the domain and range?
What is C when F = 40Ā°?
48. Profit The profit from the production and sale of a product is , where x represents the number of units produced and sold. Give
The profit from the production and sale of 2000 units.
The value of P(5000)
The meaning of P(5000).
49E50E51E52. Shipping restrictions If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by , where x is the length of each side of the cross section (in inches).
Is V a function of x?
If V = V(x), find V(10) and V(20).
What restrictions must be placed on x(the domain) so that the problem makes physical sense?
53. Profit Suppose that the profit from the production and sale of x units of a product is given by
In addition, suppose that for a certain month, the number of units produced on day t of the month is
Find to express the profit as a function of the day of the month.
Find the number of units produced, and the profit, on the fifteenth day of the month.
54. Fish species growth For many species of fish, the weight W is a function of the length L that can be expressed by
Suppose that for a particular species k = 0.02, that for this species the length(in centimeters) is a function of the number of years t the fish has been alive, and that this function is given by
Find to express W as a function of the age t of the fish.
55E56E57. Fencing a lot A farmer wants to fence the perimeter of a rectangular lot with an area of 1600 square feet. If the lot is x feet long, express the number of feet L of fence needed as a function of x.
58. Cost A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.00 per square foot and the material for the top costs $1.50 per square foot, express the total cost of material for the box as a function of x.
59. Revenue An agency charges $100 per person for a trip to a concert if 30 people travel in a group. But for each person above the 30, the amount charged each traveller will be reduced by $2. If x represents the number of people above the 30, write the agencyās revenue R as a function of x.
60. Revenue A company handles an apartment building within 50 units. Experience has shown that if the rent for each of the units is $720 per month, all of the units will be filled, but one unit will become vacant for each $20 increase in the monthly rate. If x represents the number of $20 increases, write the revenue R from the building as a function of x.
1. Find the slope of the line throughand.
If a line has slope, then the line is. If a line has an undefined slope, then the line is.
3CP4CP5CP1E2E3E4E5E6E7E8E9E10E11E12E13. What is the rate of change of the function whose graph is a line passing through?
14. What is the rate of change of the function whose graph is a line passing through?
15E16E17EIn Problems 17-24, find the slope and y-intercept and then graph each equation.
In Problems 17-24, find the slope and y-intercept and then graph each equation.
19.
20E21E22EIn Problems 17-24, find the slope and y-intercept and then graph each equation.
24EIn Problems 25-28, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.
25. Slope and y-intercept
26EIn Problems 25-28, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.
27. Slope and y-intercept
In Problems 25-28, write the slope-intercept form of the equation of the line that has the given slope and y-intercept. Then graph the line.
28. Slope and y-intercept
In Problems 29-34, write the equation of the line that passes through the given point and has the given slope. Then graph the line.
29. with slope
In Problems 29-34, write the equation of the line that passes through the given point and has the given slope. Then graph the line.
30. with slope
31EIn Problems 29-34, write the equation of the line that passes through the given point and has the given slope. Then graph the line.
32. with slope
In Problems 29-34, write the equation of the line that passes through the given point and has the given slope. Then graph the line.
33. with undefined slope
In Problems 29-34, write the equation of the line that passes through the given point and has the given slope. Then graph the line.
34. with 0 slope
In Problems 35-40, write the equation of each line described or shown.
35. Through and
36E37E38E39E40E41E42E43E44E45E46. Write the equation of the line passing throughthat is parallel to.
47E48E49E