Skip to main content

Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Mathematical Applications for the Management, Life, and Social Sciences

50. U.S population Using Social Security Administration data for selected years from 1950 and projected to 2050, the U.S. population (in millions) can be described by Where t is the number of years past 1950. Findand explain its meaning. Find the slope and explain its meaning. Graph this function for. Internet users The percent of the U.S. population with Internet service can be described by y=1.36x+55.98 where x is the number of years past 1990 (Source: Jupiter Media Metrix). (a) Find the slope and y-intercept of this equation. (b) What interpretation could be given to the slope? (c) Graph the function.52E 53E 54. Temperature-humidity models Two models for measuring the effects of high temperature and humidity are the Summer Simmer Index and the Apparent Temperature. For an outside temperature of, these indices relate the relative humidity, H (expressed as a decimal), to the perceived temperature as follows. Summer Simmer: Apparent temperature: For each index, find the point that corresponds to a relative humidity of. For each point in part (a), write a sentence that explains its meaning. Graph both equations for . 55E 56. Gross domestic product The U.S. gross domestic product (GDP), y, for the years from 2011 and projected to 2021 is given by Where x is the number of years past 1990 and y is in billions of dollars (Source: Social Security Administration). What is the slope of the graph of this function? Interpret the slope as a rate of change. 57. Residential electric costs An electric utility company determines the monthly bill for a residential customer by adding an energy charge of 8.38 cents per kilowatt-hour to its base charge ofper month. Write an equation for the monthly charge y in terms of x, the number of kilowatt-hour used. 58. Residential heating costs Residential customers who heat their homes with natural gas have their monthly bills calculated by adding a base service charge of per month and an energy charge ofcents per hundred cubic feet. Write an equation for the monthly charge y in terms of x, the number of hundreds of cubic feet used. 59. Civilian workforce The size of the U.S. civilian workforce for the years from 1950 and projected to 2050 can be approximated by a linear equation determined by the line connecting the two pointsand, where the x-coordinate is the year and the y-coordinate is the number in the civilian workforce (in millions) in year x (Source: U.S. Bureau of Labour Statistics). Write the equation of the line connecting the two points. Interpret the slope of this line as a rate of change. 60. Pension plans According to USA Today most pensions for state legislators are based on the product of the legislator’s years of service, compensation, and a multiplier (usually betweenand). When the multiplier is, a state legislator’s pension is calculated with a formula such as the following: “ of average final compensation multiplied by the years of credited service” Let p represent annual retirement pension; y, years of service; and c, average final compensation. For someone with average final compensation of, write the linear equation that gives p in terms of y. For someone intending to retire after 30 years, write the linear equation that gives p in terms of c. 61. Consumer price index The projected consumer price index (CPI) for the years 2020 to 2050 can be approximated by a linear equation determined by the line connecting the two pointsand, where the x-coordinate is the year and the y-coordinate is the price consumers pay in year x for goods that costin 2012 (Source: Social Security Administration). Write the equation of the line connecting these two points to find a linear model for these data. Interpret the slope of this line as a rate of change. 62. Drinking and driving The following table gives the number of drinks and the resulting blood alcohol percent for a 180-pound man legally considered driving under the influence (DUI) Number of drinks 5 6 7 8 9 10 Blood Alcohol Percent 0.11 0.13 0.15 0.17 0.19 0.21 Source: Pennsylvania Liquor Control Board Is the average rate of change of the blood alcohol percent with respect to the number of drinks a constant? Use the rate of change and one point determine by a number of drinks and the resulting blood alcohol percent to write the equation of a linear model for these data. Verify that the values in the table fit the model. 63. Population effects It has been estimated that a certain stream can support fish if it is pollution-free. It has further been estimated that for each ton of pollutants in the stream, 1700 fewer fish can be supported. Assuming that the relationship is linear, write the equation that gives the population of fish p in terms of the tons of pollutants x. 64. Age-sleep relationship Each day, a young person should sleep 8 hours plus hour for each year the person is under 18 years of age. Assuming that the relation is linear, write the equation relating hours of sleep y and age x. 65. Insulation R-values The R-value of insulation is a measure of its ability to resist heat transfer. For fiberglass insulation, inches is rated at R-11 and 6 inches is rated as R-19. Assuming that this relationship is linear, write the equation that gives the R-value of fiberglass insulation as a function of its thickness t (in inches). 66. Depreciation Suppose the cost of a business property is and a company wants to use a straight-line depreciation schedule for a period of 240 months. If y is the value of this property after x months, write the linear equation of this depreciation schedule. 67E Use a graphing calculator and the standard viewing window to graph the following. 2CP 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E In Problems 35-38, use the x-intercept method to find one solution of each equation. 39E 40E Consumer expenditure Suppose that the consumer expenditure E (in dollars) depends on the market price p per unit (in dollars) according to Graph this equation with a graphing calculator and the window Because E represents consumer expenditure, only values of have meaning. For what p-values is? 44E 45E Learning rate In a study using foreign language vocabulary words, the learning rate (in words per minute) was found to depend on the number of words already learned, according to the equation Use the intercepts to determine a window and then graph the equation for . Is the learning rate increasing or decreasing? Explain why your answer makes sense in the context of the problem. Elderly men in the workforce Using data from 1920 and projected to 2030, the percent P of men 65 years of age or older in the labor force can be modeled by P=0.000078x30.0107x20.182x+64.68 where x is the number of years past 1900 (Source: U.S. Census Bureau). (a) What *-min and *-max should you use to view this graph for values representing 1900 to 2030? (b) If P-min = 0, use a table to determine a value for P-max that would show a complete graph of the model. (c) Graph this equation. (d) Write a sentence that describes the percent of men 65 years of age or older in the workforce.48E 49E Pollution Suppose the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is modeled by Where Use the restriction on p and experiment with a C- range to obtain an accurate graph of the equation with a graphing utility. Describe what happens to C as p gets close to 100. The point lies on the graph of this equation. Explain the meaning of the coordinates. Explain the meaning of the p-intercept. 51E 52E Solve by substitution: 2CP 3CP 4CP 1E 2E 3E 4E 5E 6E 7E 8E In Problems 7-10, solve the systems of equations by substitution. 10E In Problems 7-10, solve the systems of equations by substitution. In Problems 7-10, solve the systems of equations by substitution. 13E In Problems 11-22, solve each system by elimination or by any convenient method. 15E In Problems 11-22, solve each system by elimination or by any convenient method. 17E 18E 19E In Problems 11-22, solve each system by elimination or by any convenient method. In Problems 11-22, solve each system by elimination or by any convenient method. 22E In Problems 11-22, solve each system by elimination or by any convenient method. 24E Use a graphing calculator or Excel to find the solution of each system of equations in Problems 23-26. 26E 27E 28E 29E Use the left-to right elimination method to solve the system in Problems 27-32. 31E 32E 33E 34E Temperature and travelling When U.S citizens travel abroad, they need some understanding of Celsius temperature readings-does one need mittens if the temperature will be 20o C? A quick conversion formula often used by tour guides to give a rough Fahrenheit equivalent for a Celsius reading is F=2C+30 Tourist formula The exact conversion formula relating these readings is F=1.8C+32 Scientific formula At what temperature, Fahrenheit and Celsius, do these formulas agree? As the Celsius temperature rises above the reading found in part (a), does the tourist formula overestimate or underestimate the actual Fahrenheit temperature? How can you tell this from the two given formulas?Population distribution Using U.S Census Bureau data (and projections to 2050), the percent of the U.S population that is Black B(x) and Hispanic H(x) can be described by B(x)=0.057x+12.3 and H(x)=0.224x+9.01 Where x is the number of years past 1990. In what year were the percents of these groups equal? What was the percent of each ? Do these models indicate that there were more Blacks or more Hispanics in 2012?Pricing A concert promoter needs to make $42,000 from the sale of 1800 tickets. The promoter charges $20 for some tickets and $30 for the others. Let x represents the number of $20 tickets and y represents the number of $30 tickets. Write an equation that states that the sum of the tickets sold is 1800. How much money is received from the sale of $20 tickets? How much money is received from the sale of $30 tickets? Write an equation that states that the total amount received from the sale is $42,000. Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $42,000.Rental income A woman has $500,000 invested in two rental properties. One yields an annual return of 10% on her investment, and the other returns 12% per year on her investment. Her total annual return from the two investments is $53,000. Let x represent the amount of the 10% investment and y represent the amount of the 12% investment. Write an equation that states that the sum of the investments is $500,000. What is the annual return on the 10% investment? What is the annual return on the 12% investment? Write an equation that states that the sum of the annual returns is $53,000. Solve these two equations simultaneously to find how much is invested in each property.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 would like to have a income of $20,000 per year from her investments. How much should she invest at each rate?Loans A bank lent $237,000 to a company tor the development of two products. If the loan for product A was for $69,000 more than that for product B, how much was lent for each product?Rental income A woman has $470,000 invested in two rental properties. One yields 10% on the investment, and the other yields 12%. Her total income from them is $51,000. How much is her income from each property?Loans Mr. Jackson borrowed money from his bank and on his life insurance to start a business. His interest rate on the bank loan was 10%, and his rate on the insurance loan was 12%. If the total amount borrowed was $100,000 and his total yearly interest payment was $10,900, how much did he borrow from the bank?41. Nutrition Each ounce of substance A supplies 5% of the nutrition a patient needs. Substance B supplies 12% of the required nutrition per ounce. If digestive restrictions require that the ratio of substance A to substance B be 3/5, how many ounces of each should be in the diet to provide 100% of the required nutrition? 42. Nutrition A glass of skim milk supplies 0.1 mg of iron and 8.5 g of protein. A quarter pound of lean red meat provides 3.4 mg of iron and 22 g of protein. If a person on a special diet is to have 7.15 mg of iron and 73.75 g of protein, how many glasses of skim milk and how many quarter-pound servings of meat would provide this? 43. Bacterial growth Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 10,600 units of the first nutrient and 19,650 units of the second nutrient. Each bacterium of species A requires 2 units of the first nutrient and 3 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 4 units of the second. What populations of each species can coexist in the environment so that all the nutrients are consumed each day? 44. Botany A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centi-meters of each solution should be mixed to obtain 25 cc of a 28% solution? 45. Medications A nurse has two solutions that contain different concentrations of a certain medication. One is a 20% concentration, and the other is a 5% concentration. How many cubic centimeters of each should he mix to obtain 10 cc of a 15.5% solution? 46. Medications Medication A is given every 4 hours, and medication B is given twice each day. The total intake of the two medications is restricted to 50.6 mg per day for a certain patient. If the ratio of the dosage of A to the dosage of B is 5 to 8, find the dosage for each administration of each medication. 47. Pricing A concert promoter needs to take in $760,000 on the scale of 16,000 tickets. If the promoter charges $40 for some tickets and $60 for others, hoe many of each type must be sold to yield the $760,000? 48. Pricing A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $3.30 per pound, how many pounds each of peanuts and cashews should be used to make 100 pounds of the mix? 49. Nutrient solutions How many cubic centimeters of a 20% solution of a nutrient must be added to 100 cc of a 2% solution of the same nutrient to make a 10% solution of the nutrient? 50. Mixtures How many gallons of washer fluid that is 13.5% antifreeze must a manufacturer add to 200 gallons of washer fluid that is 11% antifreeze to yield washer fluid that is 13% antifreeze? 51. Nutrition Each ounce of substance A supplies 5% of the nutrition a patient needs. Substance B supplies 15% of the required nutrition per ounce, and substance C supplies 12% of the required nutrition per ounce. If digestive restrictions require that substances A and C be given in equal amounts and the amount of substance B be one-fifth of either of these other amounts, find the number of ounces of each substance that should be in the meal to provide 100% of the required nutrition. 54E 53. Social services A social agency is charged with providing services to three types of clients: A, B, and C. A total of 500 clients are to be served, with $150,000 available for counseling and $100,000 available for emergency food and shelter. Type A clients require an average of $200 for counseling and $300 for emergencies, type B clients require an average of $500 for counseling and $200 for emergencies, and type C clients require an average of $300 for counseling and $100 for emergencies. How many of each type of client can be served? 56E Suppose that when a company produces its produces its product, fixed costs are $12,500 and variable cost per item is $75. Write the total cost function if represents the number of units. Are fixed costs equal to ? Suppose the company in Problem 1 sells its product for $175 per item. Write the total revenue function. Find and give its meaning. (a) Give the formula for profit in terms of revenue and cost. (b) Find the profit function for the company in problems1 and 2 4CP 5CP 6CP Suppose a calculator manufacturer has the total cost function and the total revenue function . What is the equation of the profit function for the calculator? What is the profit on 3000 units? 2E Suppose a ceiling fan manufacturer has the total cost function and the total revenue function . What is the equation of the profit function for this commodity? What is the profit on 30 units? Interpret your result. How many fans must be sold to avoid losing money? Suppose a computer manufacturer has the total cost function and the total revenue function. What is the equation of the profit function for this commodity? What is the profit on 351 items? How many items must be sold to avoid losing money? TOTAL COST, TOTAL REVENUE, AND PROFIT A linear cost function is C(x)=5x+250. (a) What are the slope and the C-intercept? (b) What is the marginal cost, and what does it mean? (c) How are your answers to parts (a) and (b) related? (d) What is the cost of producing one more item if 50 are currently being produced? What is it if 100 are currently being produced?TOTAL COST, TOTAL REVENUE, AND PROFIT A linear cost function is C(x)=27.55x+5180. (a) What are the slope and the C-intercept? (b) What is the marginal cost, and what does it mean? (c) How are your answers to parts (a) and (b) related? (d) What is the cost of producing one more item if 50 are currently being produced? What is it if 100 are currently being produced?A linear revenue function is. What is the slope? What is the marginal revenue, and what does it mean? What is the revenue received from selling one more item if 50 are currently being sold? If 100 are being sold? A linear revenue function is. What is the slope? What is the marginal revenue, what does it mean? What is the revenue received from selling one more item if 50 are currently being sold? If 100 are being sold? 9E Given and, find the profit function. What is the marginal profit, and what does it mean? What should a firm with these cost, revenue, and profit functions do? (Hint: Graph the profit function and see where it goes.) 11E 12E Extreme Protection Inc. manufactures helmets for skiing and snow boarding. The fixed costs for one model of helmet are $6600 per month. Materials and labor for each helmet of this model are $35, and the company sells this helmet to dealers for $60 each. For this helmet, write the function for monthly total costs. Write the function for total revenue. Write the function for profit. Find and interpret each answer. Findand interpret each answer. Find the marginal profit and write a sentence that explains its meaning. TOTAL COST, TOTAL REVENUE, AND PROFIT A manufacturer of DVD players has monthly fixed costs of $9800 and variable costs of $65 per unit for one particular model. The company sells this model to dealers for $100 each. (a) For this model DVD player, write the function for monthly total costs. (b) Write the function for total revenue. (c) Write the function for profit. (d) Find C(250), R(250), and P(250) and interpret each answer. (e) Find C(400), R(400), and P(400) and interpret each answer. (0 Find the marginal profit and write a sentence that explains its meaning.The figure shows graphs of the total cost function and the total revenue function for a commodity. Label each function correctly. Determine the fixed costs. Locate the break-even point and determine the number of units sold to break even. Estimate the marginal cost and marginal revenue. A manufacturer of shower surrounds has a revenue function of and a cost function of Find the number of units that must be sold to break even. A jewelry maker incurs costs for a necklace according to If the revenue function for the necklaces is How many necklaces must be sold to break even? BREAK-EVEN ANALYSIS A small business recaps and sells tires. If a set of four tires has the revenue function R(x)=89x and the cost function C(x)=1400+75x find the number of sets of recaps that must be sold to break even.A manufacturer sells belts for $12 per unit. The fixed costs are $1600 per month, and the variable cost per unit is $8. Write the equations of the revenue and cost functions. Find the break-even point. A manufacturer sells watches for $50 per unit. The fixed cost related to this product is $10,000 per month, and the variable cost per unit is $30. Write the equations of the revenue and cost functions. How many watches must be sold to break even? (a) Write the profit function for problem 19. (b) Set profit equal to zero and solve for. Compare this -value with the break – even point from Problem 19(b). (a) Write the profit function for Problem 20. (b) Set profit equal to zero and solve for. Compare this -value with the break-even point from Problem 20(b). 23.Electronic equipment manufacturer Dynamo Electric Inc. makes several types of surge protectors. Their base Model surge protector has monthly fixed costs of $1045. This particular model wholesales for $10 each And costs $4.50 per unit to manufacture. Write the function for Dynamo’s monthly total costs. Write the function for Dynamo’s monthly total revenue. Write the function for Dynamo’s monthly profit. Find the number of this type of surge protector That Dynamo must produce and sell each month to Break even. 24.Financial Paper Inc. is a printer of checks and Forms for financial institutions. For individual accounts, Boxes of 200 checks cost $0.80 per box to print and package And self for $4.95 each. Financial Paper’s monthly fixed Costs for printing and packaging these checks for individuals Are $1245. Write the function for financial Paper’s monthly Total costs. Write the function for financial Paper’s monthly Total revenue. Write the function for Financial Paper’s monthly Profit. Find the number of orders for boxes of checks For individual accounts that financial Paper must Receive and fill each month to break even. 25.A company manufactures and sells bookcases. The Selling price is $54.90per bookcase. The total cost function Is linear, and costs amount to $50,000 for 2000 bookcases And $32,120 for 800 bookcases. Write the equation for revenue. Write the equation for total costs. Find the break-even quantity. In Problem 27 and 28, some of the graphs of total revenue total cost variable cost fixed cost and profit are shown as functions of the number of units,. Correctly label the graphs shown. Carefully sketch and label the graphs of the other functions. Explain your method. 27. In Problem 27 and 28, some of the graphs of total revenue total cost variable cost fixed cost and profit are shown as functions of the number of units,. Correctly label the graphs shown. Carefully sketch and label the graphs of the other functions. Explain your method. 28. SUPPLY, DEMAND, AND MARKET EQUILIBRIUM As the price of a commodity increases, what happens to Demand?30E The graphs of the demand function and supply function for a certain product are given below. Use these graphs to answer the questions in problem 31 and 32. (a) How many units are demanded when the price is $100? (b) How many units are supplied when the price is $100? (c) Will there be a market surplus (more supplied) or shortage (more demanded) when $100 The graphs of the demand function and supply function For a certain product are given below. Use these graphs to Answer the questions in problems 31 and 32. How many units are demanded when the price is $200? How many units are supplied when the price Is 200? Will there be a market surplus or shortage when The price is $200? 33. If the demand for a pair of shoes is given by and the supply function for it is , compare the quantity demanded and the Quantity supplied when the price is $60.Will there be a Surplus or shortfall at this price? 34. If the demand function and supply function For brand juicers are and respectively, compare the Quantity demanded and the quantity supplied When Are there surplus juicers or not enough To meet demand? 35. Suppose a certain outlet chain selling appliances has Found that for one brand of home theater, the monthly Demand is 240 when the price is $900.However,when the Price is $850 , the monthly demand is 315. Assuming that The demand function for this system is linear, write the equation For the demand function. Use p for price and q for quantity. Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2500 when the price is $4.00 each but that the demand is 3500 when the price is $3.60 each. Assuming that the demand function is linear, write its equation. Use for price and for quantity. Suppose the manufacturer of a custom board game will supply 10,000 games if the wholesale price is $15 each but will supply only 5000 if the price is $10 each. Assuming that the supply function is linear, write its equation. Use for price and for quantity. Suppose a mining company will supply 100,000 tons of ore per month if the price is $30 per ton but will supply only 80,000 tons per month if the price is $25 per ton. Assuming that the supply function is linear, write its equation. Complete Problems 39-43 using the accompanying figure, which shows a supply function and a demand function. (a) Label each function as “demand” or “supply”. (b) Label the equilibrium point and determine the price and quantity at which market equilibrium occurs. (a) If the price is $30, what quantity is demanded? (b) If the price is $30, what quantity is supplied? (c) Is there a surplus or shortage when the price is $30? How many units is this surplus or shortage? (a) If the price is $20, what quantity is supplied? (b) If the price is $20, what quantity is demanded? (c) Is there a surplus or a shortage when the price is $20?. How many units is this surplus or shortage? 42E Will a price below the equilibrium price result in a market surplus or shortage? Find the market equilibrium point for the following demand and supply functions. Demand: Supply: Find the market equilibrium point for the following demand and supply functions. Demand: Supply: Find the equilibrium point for the following supply and demand functions. Demand: Supply: Find the equilibrium point for the following supply and demand functions. Demand: Supply: Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 70 at $50 each. Assuming the supply and demand functions are linear, find the market equilibrium point.A group of retailers will buy 80 televisions from a wholesaler if the price is $350 and 120 if the price is $300. The wholesaler is willing to supply 60 if the price is $280 and 140 if the price is $370. Assuming that the resulting supply and demand functions are linear, find the equilibrium point for the market. Stutz Department store will buy 10 pairs of sunglasses if the price is $75 per pair and 30 pairs if the price is $257. The supplier of the sunglasses is willing to provide 35 pairs if the price is $80 per pair but only 5 pairs if the price is $20. Assuming that the supply and demand functions for the sunglasses are linear, find the market equilibrium point. Problems involve market equilibrium after a given tax is passed on to the consumer. Use the following figure to answer Problem and. (a) What is the amount of tax? (b) What are the original equilibrium price and quantity? (c) What are the new equilibrium price and quantity? (d) Does the supplier suffer from the tax even though it is passed on? Problems involve market equilibrium after a given tax is passed on to the consumer. Use the following figure to answer Problem and. (a) If the tax is doubled, how many units will be sold? (b) Can a government lose money by increasing taxes? Problems involve market equilibrium after a given tax is passed on to the consumer. If a tax is placed on each unit of the product of Problem, what are the new equilibrium price and quantity? 54E Problems involve market equilibrium after a given tax is passed on to the consumer. Suppose that a certain product has the following demand and supply functions. If a tax per item is levied, find the market equilibrium point after the tax. 56E 57E Problems involve market equilibrium after a given tax is passed on to the consumer. Suppose that in a certain market, the demand function for a product is given by and supply function is given by. If the government levies a tax per item, find the equilibrium price and quantity after the tax is levied. In Problem 1-10, find the real solutions to each quadratic equation. In Problem 1-10, find the real solutions to each quadratic equation. In Problem 1-10, find the real solutions to each quadratic equation. 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE For each function in Problems 19-24, find the vertex and determine if it is a maximum or minimum point, find the y-intercept and the zeros if they exist, and sketch the graph. For each function in Problems 19-24, find the vertex and determine if it is a maximum or minimum point, find the y-intercept and the zeros if they exist, and sketch the graph. 24RE 25RE [Type here] In Problems 25-30, use a graphing calculator to graph each function. Use the vertex and zeros to determine an appropriate window. Be sure to label the maximum or minimum point. 26. [Type here] 27RE 28RE 29RE In Problems 25-30, use a graphing calculator to graph each function. Use the vertex and zeros to determine an appropriate window. Be sure to label the maximum or minimum point. 30. The supply function for a product is 2pq10=0, while the demand function for the Same product is (p+10)(q+30)=7200. Find the market equilibrium point.The supply and demand for a product are given by 2p-q=50andpq=100+20q Respectively. Find the market equilibrium point.33.For the product in Problem 31,if a $22 tax is placed on production of the item, then the Supplier passes this tax on by adding $22 to his selling price. Find the new equilibrium point For this product when the tax is passed on.(The new supply function is given by .) 34RE In Problems 33-36, a graph is given. Use the graph to locate the vertex, determine the zeros, and match the graph with one of A, B, C, or D. 35. 36RE 37. Sketch a graph of each of the following basic functions. (a) (b) (c) 38RE 39RE In Problems 40 and 41 ,graph each function. 40. 41RE 42RE 43RE 44RE 45RE 46RE 47RE 48RE 49.Profit The profit for a product is given by Where x is the number of units produced and sold , Break-even points will occur At values of x where How many units will give a break-even point for the Product? 50RE 51RE 52RE 53RE 54. Market equilibrium (a) Suppose the supply function for a product is and the demand function is. Sketch the first-quadrant portion of the graph of each function. Use the same set of axes for both and label the market equilibrium point. (b) Use algebraic method to find the equilibrium price and quantity. 55RE 56RE Break-even points If total costs for a product are given by and total revenues are given by , find the break-even quantities. Break-even points If total costs for a commodity are given by and total revenues are given by , find the break-even quantities. 59RE 60RE Maximum profit Given and , find the level of production that gives maximum profit and find the maximum profit. Break-even and profit maximization A certain company has fixed costs of $15,000 for its product and variable costs given by dollars per unit, where is the total number of units. The selling price of the product is given by dollars per unit. Formulate the functions for total cost and total revenue. Find the break-even quantities. Find the level of sales that maximizes revenue. Form the profit function and find the level of production and sales that maximizes profit. Find the profit (or loss) at the production levels found in parts (c) and (d). 63. Diabetes The rise of adult diabetes in the United States is a growing concerned for health professionals. Using Centers for Disease Control and Prevention data for selected years from 2010 and projected to 2050, the percent of US adults with diabetes can be modeled by the function, where t is the number of years past 2000. (a) What type of function is this? (b) What does the function predict as the percent of US adults with diabetes in the year 2020? (c) Find and write a sentence that explains its meaning. 64RE 65RE 66RE 67RE 68. Average annual wage The tables below give Social Security Administration data for the U.S. average annual wage from and projected to and for selected years from and projected to . (a) Make a scatter plot of each of these data sets with as the number of years past . (b) Decide which one function type could be used as a model for both data sets and find the two models. Let be the model for the data to and be the model for data to . Report both models with significant digit coefficients. (c) How well do the reported models agree for the data points for and ? (d) When does each reported model predict that the average annual wage will reach ? Data to 2021 (in dollars) Data to 2050 (in thousands of dollars) 69RE 70RE 1T 2T 3T 4T Which of the following three graphs is the graph of ? Explain your choice. 6T 7T 8T 9T 10T 11T 12T 13T 14T 15T 16T Suppose the supply and demand functions for a product are given by and respectively. Find the equilibrium price and quantity. Suppose a company’s total cost a product is given by and the total revenue for the product is given by where x is the number of units produced and sold. Find the profit function. Determine the number of units at which the profit for the product is maximized and find the maximum possible profit. Find the break-even point(s) for the product. 19T 20T 1EAGP1 2EAGP1 3EAGP1 4EAGP1 5EAGP1 6EAGP1 7EAGP1 1EAGP2 2EAGP2 3EAGP2 4EAGP2 5EAGP2 6EAGP2 7EAGP2 8EAGP2 The factoring method for solving a quadratic equation is based on the ________ product property. Hence, to solve a quadratic equation by factoring, one side of the equation must equal ________.

Page: [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]