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

Solve the following equations by factoring. 3CP 4CP 1E 2E 3E 4E In Problems 5-14, solve each question by factoring. x24x=12 6E In Problems 5-14, solve each question by factoring. 94x2=0 8E In Problems 5-14, solve each question by factoring. x=x2 10E In Problems 5-14, solve each question by factoring. 4t24t+1=0 12E In Problems 15-20, solve each equation using the quadratic formula. Give real answers (a) exactly and (b) rounded to two decimal places. x24x=4 In Problems 15-20, solve each equation using the quadratic formula. Give real answers (a) exactly and (b) rounded to two decimal places. x2+7=6x In Problems 15-20, solve each equation using the quadratic formula. Give real answers (a) exactly and (b) rounded to two decimal places. 2w2+w+1=0 16E In Problems 21-26, find the exact real solutions to each equation, if they exist. y2=7 18E 19E 20E In Problems 21-26, find the exact real solutions to each equation, if they exist. (x+4)2=25 In Problems 21-26, find the exact real solutions to each equation, if they exist. (x+1)2=2 In Problems 27-36, use any method to find the exact real solutions, if they exist. x2+5x=21+x In Problems 27-36, use any method to find the exact real solutions, if they exist. x2+17x=8x14 In Problems 27-36, use any method to find the exact real solutions, if they exist. w28w24=0 26E 27E 28E In Problems 27-36, use any method to find the exact real solutions, if they exist. (x1)(x+5)=7 30E 31E 32E 33E 34E In problems 37-42, solve each equation using a graphing utility. 36E In problems 37-42, solve each equation using a graphing utility. 38E 39E 40E In Problems 43-46, multiply both sides of the equation by the LCD and solve the resulting quadratic equation. xx1=2x+1x1 42E 43E 44E Applications Profit If the profit from the sale of x units of a product is P=90x200x2 what level(s) of production will yield a profit of $1200?Profit If the profit from the sale of x units of a product is P=16x0.1x2100, what level(s) of production will yield a profit of $180?Profit Suppose the profit from the sale of x units of a product is P=640018x2400. (a) What level(s) of production will yield a profit of $61,800? (b) Can a profit of more than $61,800 be made?Profit Suppose the profit from the sale of x units of a product is P=50x3000.01x2. (a) What level(s) of production will yield a profit of $250? (b) Can a profit of more than $250 be made?Flight of a ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height if the ball is given by S=100+96t16t2 feet where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?Flight of a ball A tennis ball is thrown into the air from the top of a hotel that is 350 feet above the ground. The height of the ball from the ground is given by D(t)=16t2+10t+350 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground?Wind and pollution The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by P=250.01s2 Find the value(s) of s that will make p=0. What value of s from part (a) makes sense in the context of this application? What does p=0 mean in this application?Drug sensitivity The sensitivity S to a drug is related to the dosage size by S=100xx2 where x is the dosage size in milliliters. What dosage(s) will yield 0 sensitivity? Explain what your answer in part (a) might mean.57. Corvette acceleration The time t, in seconds , it takes a Corvette to accelerate to mph can be described by (Source: Motor Trend). How fast is the Corvette going After 8.99 seconds? Give your answer to the nearest tenth. 59. Marijuana use For the years since 2001 , the percent Of high school seniors who have tried marijuana can be Considered as a function of time according to Where is the number of years past 2000(Source: National Institute on Drug Abuse). In what year after 2000 is the percent predicted to reach if this function Remains valid? 56E 61. Percent profit Ace Jewelry Store sold a necklace for If the percent profit (based on cost)equals the Cost of the necklace to the store, how much did the Store pay for it? Use Where is profit and is cost. Tourism spending The global spending on travel and tourism (in billions of dollars) can be described by the equation y=0.787x211.0x+290 where x equals the number of years past 1990 (Source: World Tourism Organization). Find the year after 1990 in which spending is projected to reach $1000 billion.59E 64. Velocity of blood Because of friction from the walls of An artery , the velocity of a blood corpuscle in an artery Is greatest at the center of the artery and decreases as The distance from the centre increases. The velocity Of the blood in the artery can be modeled by the function Where is the radius of the artery and is a constant That is determined by the pressure , the viscosity of The blood, and the length of the artery. In the case Where and centimeters, the velocity is centimeters per second. What distance would give a velocity of cm/sec? What distance would give a velocity of cm/sec? (c)What distance would give a velocity of Cm/sec? Where is the blood corpuscle? 65. Body-heat loss The model for body-heat loss depends On the coefficient of convection ,which depends on Wind speed according to the equation Where is in miles per hour. Find the positive Coefficient of convection when the wind speed is (a) (b) (c)What is the change in for a change in speed from to 66. Depth of Fissure A fissure in the earth appeared after An earthquake. To measure its vertical depth, a stone Was dropped into it, and the sound of the stone’s impact was heard 3.9 seconds later. The distance (in feet )the stone fell is given by and the distance (in feet) the sound traveled is given by .In these equations , the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is seconds, find the depth of the fissure. Name the graph of a quadratic function. (a) What is the coordinate of the vertex of ? (b) For , what is the coordinate of the vertex? What is the coordinate of the vertex? 3CP 4CP 5CP In Problems 1-6,(a)find the vertex of the graph of the Equation,(b)determine whether the vertex is a maximum Or minimum point, (c)determine what value of x gives The optimal value of the function, and (d) determine the Optimal (maximum or minimum)value of the function. 1. 2E In Problems 1-6,(a) find the vertex of the graph of the Equation,(b) determine whether the vertex is a maximum Or minimum point,(c)determine what value of x gives The optimal value of the function ,and (d)determine The optimal (maximum or minimum )value of the function. In Problem 1-6,(a)find the vertex of the graph of the Equation,(b) determine whether the vertex is a maximum Or minimum point,(c) determine what value of x gives The optimal value of the function, and (d) determine the Optimal (maximum or minimum) value of the function. In Problems 1-6,(a) find the vertex of the graph of the Equation,(b) determine whether the vertex is a maximum Or minimum point,(c) determine what value of x gives The optimal value of the function, and (d) determine the Optimal(maximum or minimum) value of the function. 5. In Problems 1-6,(a) find the vertex of the graph of the Equation,(b)determine what value of x gives the optimal Value of the function, and (d)determine the optimal (maximum or minimum )value of the function. In Problems 7-12,determine whether each function’s Vertex is a maximum point or a minimum point and find The coordinates of this point. Find the zeros, if any exist, and The y-intercept. Then sketch the graph of the function. In Problems7-12,determine whether each functions vertex Is a maximum point or a minimum point and find the Coordinates of this point. Find the zeroes ,if any exist, and The y-intercept. Then sketch the graph of the function. In Problems 7-12,determine whether each function’s Vertex is a maximum point or a minimum point and find the Coordinates of this point. Find the zeroes, if any exist, and The y-intercept. Then sketch the graph of the function. In Problem 7-12, determine whether each function’s vertex is a maximum point or a minimum point and find the coordinates of this point. Find the zeroes, if any exist, and the -intercept. Then sketch the graph of the function. 11E 12E 13E 14E 15E 16E 17E 18E 19E In Problems , graph each function with a graphing utility. Use the graph to find the vertex and zeros. Check your results algebraically. 21E In Problem 21 and 22, find the average rate of change of the function between the given values of x. In Problems , find the vertex and zeros and use them to determine a window for a graphing calculator that includes these values; graph the function with that window. 24E 25E 26E 27E 28E 29E 30E Profit The daily profit from the sale of a product is given by P=16x0.1x2100 dollars. (a) What level of production maximizes profit? (b) What is the maximum possible profit?Profit The daily profit from the sale of x units of a product is P=80x0.4x2200 dollars. (a) What level of production maximizes profit? (b) What is the maximum possible profit?33. Crop Yield The yield in bushels from a grove of orange trees is given by , where x is the number of orange trees per acre. How many trees will maximize the yield? 34. Stimulus-response One of the early results in psychology relating the magnitude of a stimulus x to the magnitude of a response y is expressed by the equation where k is an experimental constant. Sketch this graph for . Drug Sensitivity The sensitivity S to a drug is related to the dosage (in milligrams) by- Sketch the graph of this function and determine what dosage gives maximum sensitivity. Use the graph to determine the maximum sensitivity. 36. Maximizing an enclosed area Iffeet of fence Is used to enclose a rectangular yard, then the resulting Area is given by Where feet is the width of the rectangle and Feet is the length. Graph this equation and determine The length and width that give maximum area. Photosynthesis The rate of photosynthesis R for a certain plant depends on the intensity of light , in lumens, according to Sketch the graph of this function and determine the intensity that gives the maximum rate. 38. Projectiles A ball thrown vertically into the air has its Height above ground given by Where is in seconds and is in feet . Find the maximum Height of the ball. Projectiles Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by and where x is the horizontal distance and y is the vertical distance, both is feet. Determine which projectile goes higher by locating the vertex of each parabola. 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 higher 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 elbow and its velocity v (in centimeter per second) is given by Solve this equation for h and graph the result, using the velocity as the independent variable. 41E 42E Apartment rental The owner of an apartment building can rent all 50 apartments if she charges $600 per month, but she rents one fewer apartment for each $20 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $600, $620, and $640. (b) Does her revenue from the rental of the apartments increase or decrease as she increases the rent from $600 to $640? (c) Write an equation that gives the revenue from rental of the apartments if she makes x increases of $20 in the rent. (d) Find the rent she should charge to maximize her revenue. Revenue The owner of a skating rink rents the rink for parties at if or fewer skaters attend , so that the cost per person is if attend . For each 5 skaters above 50, she reduces the price per skater by Construct a table that gives the revenue generated if , , and skaters attend. Does the owner’s revenue from the rental of the rink increase or decrease as the number of skaters increases from to ? Write the equation that describes the revenue for parties with more than skaters. Find the number of skaters that will maximize the revenue. Pension resources The Pension Benefit Guaranty Corporation is the agency that insures pension . The figure shows one study’s projection for the agency’s total resources, initially rising (from taking over the assets of failing plans) but then falling (as more workers retire and payouts increase). What kind of function might be used to model the agency’s total resources ? If a function of the form were used to model these total resources. would have or ? Explain. If the model from part (b) used as the number of years past , explain way the model would have and . 46E Health care costs per capita Rising health care costs are a growing concern for everyone in the United States. Using U.S.Centers for Medicare and Medicail Services data from and projected to , U.S . per capita health care costs can be modeled by where is the number of years past . Use this equation to find , to the nearest dollars , the average rate of change of U.S. per capita health care costs from to and from to Women in the workforce Using U.S. Census Bureau data for selected years from and projected to , the percent of the total workforce that is female is given by where is the number of years past Graph the function From the equation , identify the maximum point on the graph of . In what year is the percent of women workers projected to be at its maximum , according to this model? 49E E-commerce Online sales in the United States are expected to exceed billions by . Using data from to, the revenue. in billions of dollars, can be describe by where is the number of years past . Use this function in Problem and (Source: U.S. Census Bureau Forrester Research, Inc.) The data starts is , at , and the function may not apply before then. The graph has a minimum points; where is this points? The point of intersection of the revenue function and the cost function is _________. If and , finding the break-even points requires solution of what equation? Find the break-even points. 3CP 4CP BREAK-EVEN POINTS AND MAXIMIZATION 1.The total costs for a company are given by And the total revenues are given by Find the break-even points. 2. If a firm has the following cost and revenue functions, Find the break-even points. 3.If a company has total costs And total revenues given by find the break-even points. 4. If total costs are and total revenues Are ,find the break-even points. Given that profit is P(x)=11.5x-0.1x2-150 And that production is restricted to fewer than 75 units, Find the break-even points.6.If the profit function for a firm is given by And limitations on space require that production be less than 100 Units, find the break-even points. BREAK-EVEN POINTS AND MAXIMIZATION Find the maximum revenue for the revenue function R(x)=385x0.9x2.8.Find the maximum revenue for the revenue function . 9.If in a monopoly market the demand for a product is and the revenue function is where x is the Number of units sold ,what price will maximize revenue? 10.If in a monopoly market the demand for a product is and the revenue is where x is the number of Units sold, what price will maximize revenue? The profit function for a certain commodity is Find the level of production that yields maximum profit and find the maximum profit. The profit function for a firm making widgets is Find the number of units at which maximum profit is achieved and find the maximum profit. (a) Graph the profit function . (b) Find the vertex of the graph. Is it a maximum point or a minimum point? (c) Is the average rate of change of this function from to positive or negative? (d) Is the average rate of change of this function from to positive or negative? (e) Does the average rate of change of the profit get closer to or farther from 0 when is closer to 400? 14E (a) Form the profit function for the cost and revenue functions in Problem 3 and find the maximum profit. (b) Compare the level of production to maximize profit with the level to maximize revenue (see Problem 7). Do they agree? (c) How do the break-even points compare with the zeros of ? 16E 17. Suppose a company has fixed costs of and variable cost per unit of dollars, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. (a) Find the break-even points. (b) Find the maximum revenue. (c) Form the profit function from the cost and revenue functions and find maximum profit. (d) What price will maximize the profit? 18. Suppose a company has fixed costs of and variable cost per unit of dollars, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. (a) Find the break-even points. (b) Find the maximum revenue. (c) Form the profit function from the cost and revenue functions and find maximum profit. (d) What price will maximize the profit? 19E BREAK-EVEN POINTS AND MAXIMIZATION Assume that sales revenues for Continental Divide Mining can be modeled by R(t)=0.031t2+0.776t+0.179 where t is the number of years past 2003. (a) Use the function to determine the year in which maximum revenue occurs and the maximum revenue it predicts. (b) Check the result from (a) against the data in the table. (c) Graph R(t) and the data points from the table. (d) Write a sentence to describe how well the function fits the data.BREAK-EVEN POINTS AND MAXIMIZATION Assume that costs and expenses for Continental Divide Mining can be modeled by C(t)=0.012t2+0.492t+0.725 where t is the number of years past 2003. (a) Use R(t) as given in Problem 20 and form the profit function (as a function of time). (b) Use the function from (a) to find the year in which maximum profit occurs. (c) Graph the profit function from (a) and the data points from the table. (d) Through the decade from 2011 to 2021, does the function project increasing or decreasing profits? Do the data support this trend (as far as it goes)? (e) How might management respond to this kind of projection?In Problems 22-24, a supply function and a demand function are given. (a) Sketch the first-quadrant portions of those functions on the same set of axes. (b) Label the market equilibrium point. (c) Algebraically determine the market equilibrium point. 22. Supply: Demand: In Problems 22-24, a supply function and a demand function are given. (a) Sketch the first-quadrant portions of those functions on the same set of axes. (b) Label the market equilibrium point. (c) Algebraically determine the market equilibrium point. 23. Supply: Demand: In Problems 22-24, a supply function and a demand function are given. (a) Sketch the first-quadrant portions of those functions on the same set of axes. (b) Label the market equilibrium point. (c) Algebraically determine the market equilibrium point. 24. Supply: Demand: 25. If the supply function for a commodity is and the demand function is, find the equilibrium quantity and equilibrium price. If the supply function for a commodity is and the demand functions is find the equilibrium quantity and equilibrium price. If the demand function for a commodity is given by the equation and the supply function is given by the equation find the equilibrium quantity and equilibrium price. If the supply and demand functions for a commodity are given and respectively, find the price and quantity that will result in market equilibrium. If the supply and demand functions for a commodity are given and what is the equilibrium price and what is the corresponding number of units supplied and demanded? If the supply and demand functions for a certain product are given by the equations and respectively, find the price and quantity that give market equilibrium. The supply function for a product is , while the demand function for the same product is . Find the market equilibrium point. The supply and demand for a product are given by and , respectively. Find the market equilibrium point. 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 .) 34E All constant functions [such as ] have graphs that are ________. Which of the following are polynomial functions? A third-degree polynomial can have at most _____ turning points. 4CP 5CP In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problems 1-12, match each of the function with one of the graphs labeled (a)-(1) shown following these functions. Recognizing special features of certain types of functions and plotting points for the functions will be helpful. In problem 13, decide whether each function whose graph is shown is the graph of a cubic (third-degree) or quartic (fourth-degree) function. In problem 14, decide whether each function whose graph is shown is the graph of a cubic (third-degree) or quartic (fourth-degree) function. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 15. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 16. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 17. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 18. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 19. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 20. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 20. In Problems 15-22, match each equation with the correct graph among those labeled (a)-(h) by recognizing shape and features of polynomial and rational functions .Use a graphing utility to confirm your choice. 20. 24E 25E 26E 27E In Problems 23-28, graph the function. 28. 29E 30E 31E 32E 33E 34. If find the following. (b) (c) (d) In Problems 35-40, (a) graph each function with a graphing utility; (b) classify each function as a polynomial function, a rational, or a piecewise defined function; (c) identify any asymptotes; and (d) use the graphs to locate turning points. 35. In Problems 35-40, (a) graph each function with a graphing utility; (b) classify each function as a polynomial function, a rational, or a piecewise defined function; (c) identify any asymptotes; and (d) use the graphs to locate turning points. 36. [Type here] In Problems 35-40, (a) graph each function with a graphing utility; (b) classify each function as a polynomial function, a rational, or a piecewise defined function; (c) identify any asymptotes; and (d) use the graphs to locate turning points. 37. [Type here] [Type here] In Problems 35-40, (a) graph each function with a graphing utility; (b) classify each function as a polynomial function, a rational, or a piecewise defined function; (c) identify any asymptotes; and (d) use the graphs to locate turning points. 38. [Type here] 39E 40E 41. Postal restrictions If a box with a square cross section is to be sent by the postal service, there are restrictions on its size such that its volume is limited by , where is the length of each side of the cross section (in inches). (a) If , find and . (b) What restrictions must be placed on (the domain) so that the problem makes physical sense? 42E 43E 44E 45. Pollution Suppose that the cost (in dollars) of removing percent of the particulate pollution from the smokestacks of an industrial plant is given by Is undefined at any - value? If so, what value? What is the domain of as given by the equation? What is the domain of in the context of the application? What happens to the cost as the percent of pollution removed approaches 100%? Average cost If the weekly total cost of producing 27 Toshiba television sets is given by C(x)=50,000+105x, where x is the number of sets produced per week, then the average cost per unit is given by C(x)=50,000+105xx (a) What is the average cost per set if 3000 sets are sold? (b) Graph this function. (c) Does the average cost per set continue to fall as the number of sets produced increases?Area If 100 feet of fence is to be used to enclose a rectangular yard, then the resulting area of the fenced yard is given by where x is the width of the rectangle. If find What restrictions must be placed on x (the domain) so that the problem makes physical sense? Water usage The monthly charge for water in a small town is given by where x is water usage in hundreds of gallons and f(x)is in dollars. Find the monthly charge for each of the following usages. 30 gallons. 3000 gallons. 4000 gallons. Graph the function for 49E Commercial electrical usage The monthly charge (in dollars) for x kilowatt hours (kWh) of electricity used by a commercial customer is given by the following function. Find the monthly charges for the following usages. (b) (c) First-class postage The postage charged for first-class mail is a function of its weight. The U.S. Postal Service uses the following table to describe the rates. Weight Increment Rate($) First ounce or fraction of an ounce Each additional ounce or fraction 0.49 0.21 Convert this table to a piecewise defined function that represents postage for letters weighing between 0 and 4 ounces, using x as the weight in ounces and P as the postage in cents. Find the domain and range of P as it is defined above. Give the domain and range of P as it is defined above. Find the postage for a 2-ounce letter and for a 2.01 ounce letter. Income tax In a given year the U.S. federal income tax owed by a married couple filing jointly can be found from the following table (Source: Internal Revenue Service, Form 1040 Instructions). Filing Status: Married Filing Jointly If taxable income Tax due Of the amount is between is over $0- $16,750 $0.00 + 10.0% $0 $16,750 - $68,000 $1,675.00 F 15.0% $16,750 $68,000- $137,300 $9,362.50 + 25.0% $68,000 $137,300 -$209,250 $26,687.50 + 28.0% $137,300 $209,250 - $373,650 $46,833.50 + 33.0% $209,250 $373,650 - Up $101,085.50 + 35.0% $373,650 (a) For incomes up to $137,300, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned. (b) Use the function to find T(70,000). (c) Find the tax due on a taxable income of $50,000. (d) A friend tells Jack Waddell not to earn any money over $68,000 because it would raise his tax rateto 25% on all of his taxable income. Test this statement by finding the tax due on $68,000 and $68,000 + $ 1. What do you conclude?53E 55E The following table gives the Social Security Trust Fund balance (in billions of dollars) for selected years from and projected to. (1) Make a scatter plot of the data with as the number of years past. Source: Social Security Administration 2CP 1E 2E In Problems 1-8, determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. 3. In Problems 1-8, determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. 4. 5E In Problems 1-8, determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. 6. 7E 8E 9E 10E In Problems 9- 16, find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. 11. quadratic 12E 13E In Problems 9- 16, find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. 14. cubic 15E In Problems 9- 16, find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation. 16. power 17E 18E 19E 20E In Problems 17-24, (a) plot the given points, (b) determine what type of function best models the data, and (c) find the equation that is the best fit for the data. 21. In Problems 17-24, (a) plot the given points, (b) determine what type of function best models the data, and (c) find the equation that is the best fit for the data. 22. In Problems 17-24, (a) plot the given points, (b) determine what type of function best models the data, and (c) find the equation that is the best fit for the data. 23. 24E 25E emission The following table gives the millions of metric tons of carbon dioxide emission in the United States for selected years from and projected to Create linear function that models these data, with as the number of years past and as the millions of metric tons of carbon dioxide emission Find the models estimate for the data point. Find and interpret slope of the linear model Disposable income Disposable income is the amount left after taxes have been paid and is one measure of the health of the economy. The following table gives the total U.S disposable income (in billions of dollars) for selected year from and projected to . Use as the number of years past and write the equation of the function that is best fit for these data. What does the model predict for the disposable income in ? Interpret slope of the model found in parts (a). Diabetes As the following table shows , projections indicate that the percent of U.S. adults with diabetes could dramatically increase. Find a linear model that fits the data in the table, with as the percent of year in . Use the model to predict the percent of U.S. adults with diabetes in . In what year does this model predict the percent of U.S adults with diabetes will reach ? Wind chill The table gives the wind chill temperature when the outside temperature is. Use as the wind speed and create q quadratic model for these data. At what wind speed does the model predict that the wind chill temperature will be lowest? Do you think the model found in part (a) is valid for ? Explain. Developing economies The developing economies’ share of the global gross domestic product (GDP) from to is shown in the following table. Find the quadratic function that best models GDP as a function of the number of year after. Use technology to find the maximum share of GDP that the developing economics can achieve, according to this model. 31E 32E 33E 34E 35E National health care The table shows the national expenditures for health care in the United States for selected years, with the projection to. Use the scatter plot with as the number of years past and as the total expenditures for the health care (in billions) to identify what type (or types) of function(s) would make a good model for these data. Find a power model and a quadratic model for the data. Which model from part (b) approximates more accurately the data point for . Use the quadratic model to predict the expenditures for national health care. 37E 38E Use the matrices below a needed to complete Problems 1-25, Find in matrix . Use the matrices below a needed to complete Problems 1-25, Find in matrix . 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE In Problems 30-36, solve each system using matrices. 32RE In Problems 30-36, solve each system using matrices. 33. 34RE 35RE 36RE 37RE 38RE 39RE 40RE 41RE 42RE 43RE 44RE

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