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All Textbook Solutions for Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 15-24, find the slope of the given line if it is defined. 3y+1=0 22E In Exercises 15-24, find the slope of the given line if it is defined. 4x+3y=7 24E In Exercises 2538, graph the given equation.[HINT: See Quick Examples 3 and 4.] y=2x1 26E 27E 28E 29E 30E 31E 32E In Exercises 2538, graph the given equation.[HINT: See Quick Examples 3 and 4.] 3x=8 34E 35E 36E 37E 38E 39E 40E 41E 42E In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example 5.] (4,3) and (5,1)44E In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example 5.] (1,1) and (1,2)46E 47E 48E 49E 50E 51E 52E In Exercises 39-58, calculate the exact slope (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do as many as you can without writing anything down except the answer. [HINT: See Quick Example 5.] (a,b) and (c,d) (ac)54E 55E 56E 57E 58E In the following figure, estimate the slopes of all line segments:60E In Exercises 61-80, find a linear equation whose graph is the straight line with the given properties. [HINT: See Example 2.] Through (1,3) with slope 3 In Exercises 61-80, find a linear equation whose graph is the straight line with the given properties. [HINT: See Example 2.] Through (2,1) with slope 2 63E 64E In Exercises 61-80, find a linear equation whose graph is the straight line with the given properties. [HINT: See Example 2.] Through (20,3.5) and increasing at a rate of 10 units of y per unit of x.66E In Exercises 61-80, find a linear equation whose graph is the straight line with the given properties. [HINT: See Example 2.] Through (2,4) and (1,1)68E 69E 70E 71E In Exercises 61-80, find a linear equation whose graph is the straight line with the given properties. [HINT: See Example 2.] Through (13,1) and parallel to the line 3x4y=8 73E 74E 75E 76E 77E 78E 79E 80E 81E Cost A soft-drink manufacturer can produce 1,000 cases of soda in a week at a total cost of $6,000 and 1,500 cases of soda at a total cost of $8,500. Find the manufacturers weekly fixed costs and marginal cost per case of soda.Cost: iPhone 5 (16 GB) If it costs Apple $2,070 to manufacture 10 iPhones per hour and $4,120 to manufacture 20 per hour at a particular plant,42 obtain the corresponding linear cost function. What was the cost to manufacture each additional iphone? Use the cost function to estimate the cost of manufacturing 40 iPhones in an hour.84E Demand Sales figures show that your company sold 1,960 pen sets each week when they were priced at $1.00 per pen set and 1,800 pen sets each week when they were priced at $5.00 per pen set. What is the linear demand function for your pen sets? [HINT: See Example 4.]Demand A large department store is prepared to buy 3,950 of your tie-dye shower curtains per month for $5 each but only 3,700 per month for $10 each. What is the linear demand function for your tie-dye shower curtains?Demand for Smartphones The following table shows worldwide sales of smartphones and their average selling prices in 2012 and 2013:44 Year 2012 2013 Selling Price ($) 385 335 Sales (millions) 720 1,010 a. Use the data to obtain a linear demand function for smartphones, and use your demand equation to predict sales if the price is lowered to $265. b. Fill in the blanks: For every_________ increase in price, sales of smartphones decrease by _________ units.88E Demand for Monorail Service: Las Vegas In 2005 the Las Vegas monorail charged $3 per ride and had an average ridership of about 28,000 per day. In December 2005 the Las Vegas Monorail Company raised the fare to $5 per ride, and average ridership in 2006 plunged to around 19,000 per day.46 a. Use the given information to find a linear demand equation. b. Give the units of measurement and interpretation of the slope. c. What would have been the effect on ridership of raising the fare to $6 per ride?Demand/or Monorail Service: Mars The Utarek monorail, which links the three urbynes (or districts) of Utarek on Mars, charged Z5 per ride47 and sold about 14 million rides per day. When the Utarek City Council lowered the fare to Z3 per ride, the number of rides increased to 18 million per day. a. Use the given information to find a linear demand equation. b. Give the units of measurement and interpretation of the slope. c. What would have been the effect on ridership of raising the fate to Z10 per ride?Pasta Imports in the 1990s During the period 1990-2001, U.S. imports of pasta increased from 290 million pounds in 1990 (t=0) by an average of 40 million pounds per year.48 a. Use this information to express y, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. b. Use your model 10 estimate U.S. pasta imports in 2005, assuming that the import trend continued.92E Net Income The net income of Amazon decreased from $0.63 billion in 2011 to $0.24 billion in 2014.49 a. Use this information to find a linear model for Amazons net income N (in billions of dollars) as a function of time t in years since 2010. b. Give the units of measurement and interpretation of the slope. c. Use the model from pan (a) to estimate the 2013 net income. (The actual 2013 net income was approximately $0.27 billion.)Operating Expenses The operating expenses of Amazon increased from $3.6 billion in 2008 to $16.3 billion in 2012.50 a. Use this information to find a linear model for Amazons operating expenses E (in billions of dollars) as a function of time t in years since 2010. b. Give the units of measurement and interpretation of the slope. c. Use the model from pan (a) to estimate the 2011 operating expenses. (The actual 2011 operating expenses were $10.9 billion.)95E 96E 97E 98E Textbook Sizes The second edition of Applied Calculus by Waner and Costeaoble was 585 pages long. By the Lime we got to the sixth edition, the book had grown to 755 pages. a. Use this information to obtain the page length L as a linear function of the edition number n. b. What are the units of measurement of the slope? What does the slope tell you about the length of Applied Calculus? c. At this rate, by which edition will the book have grown to over 1,500 pages?100E 101E 102E 103E 104E 105E 106E Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1996-2010 could be approximated by the following function of time t in years since the start of 1990:53 v(t)={400t2,200if6t153,800if15t20 How fast and in what direction was processor speed changing in 2000?Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1970-2000 could be approximated by the following function of time t in years since the start of 1970:54 v(t)={3tif0t20174t3,420if20t30 How fast and in what direction was processor speed changing in 1995?109E 110E 111E 112E 113E 114E 115E 116E 117E 118E 119E 120E 121E 122E 123E 124E 125E 126E 127E 128E 129E 130E 131E 132E 133E 134E In Exercises 1-4, compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. [HINT: See Example 1.] (1,1),(2,2),(3,4);y=x1 In Exercises 1-4, compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. [HINT: See Example 1.] (0,1),(1,1),(2,2);y=x+1 3E 4E 5E 6E In Exercises 5-8, use technology to compute the sum-of-squares error (SSE) for the given set of data and linear models. Indicate which linear model gives the better fit. (0,1),(1,3),(4,6),(5,0) a. y=0.3x+1.1 b. y=0.4x+0.9 In Exercises 5-8, use technology to compute the sum-of-squares error (SSE) for the given set of data and linear models. Indicate which linear model gives the better fit. (2,4),(6,8),(8,12),(10,0) a. y=0.1x+7 b. y=0.2x+6 9E In Exercises 9-12, find the regression line associated with the given set of points. Graph the data and the best-fit line. (Round all coefficients to four decimal places.) [HINT: See Example 2.] (0,1),(1,1),(2,2)In Exercises 9-12, find the regression line associated with the given set of points. Graph the data and the best-fit line. (Round all coefficients to four decimal places.) [HINT: See Example 2.] (0,1),(1,3),(3,6),(4,1)12E In Exercises 13 and 14, use correlation coefficients to determine which of the given sets of data is best fit by its associated regression line and which is fit worst. Is it a perfect fit for any of the data sets? [HINT: See Example 3.] a. (1,3),(2,4),(5,6) b. (0,1),(2,1),(3,4) c. (4,3),(5,5),(0,0)14E Mobile Broadband Subscriptions The following table shows the number of mobile broadband subscribers worldwide (x is the number of years since 2010):62 Year x 0 2 4 Subscribers y (millions) 800 1,600 2,300 Complete the following table, and obtain the associated regression line. (Round coefficients to one decimal place.) [HINT: See Example 2.] x y xy x2 0 800 2 1,600 4 2,300 (Sum) Use your regression equation to project the number in 2016.Fixed-Line Telephone Subscriptions The following table shows the number of fixed-line telephone subscribers in the United Kingdom (x is the number of years since 2000):63 Year x 0 5 14 Subscribers y (millions) 35 34 33 Complete the following table, and obtain the associated regression line. (Round coefficients to one decimal place.) [HINT: See Example 2.] x y xy x2 0 35 5 34 14 33 (Sum) Use your regression equation to project the number in 2015.Demand for Smartphones The following table shows worldwide sales of smartphones and their average selling prices in 2012, 2013, and 2017:64 Year 2012 2013 2017 Selling Price p ($100) 4 3 2 Sales q (billions) 0.7 1 2 Find the regression line (round coefficients to one decimal place), and use it to estimate the demand (in millions of units sold) when the selling price was $350.Demand for Smartphones The following table shows worldwide sales of smartphones and their average selling prices in 2010, 2012, and 2013:65 Year 2010 2012 2013 Selling Price p ($100) 5 4 3 Sales q (billions) 0.3 0.7 1 Find the regression line (round coefficients to one decimal place), and use it to estimate the demand (in millions of units sold) when the selling price was $450.Oil Recovery The Texas Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The following table gives the approximate number of jobs for the citizens of Texas that would be created at various levels of recovery:66 Percent Recovery ( % ) 20 40 80 100 Jobs Created (millions) 3 6 9 15 Find the regression line, and use it to estimate the number of jobs that would be created at a recovery level of 50%.20E Profit: Amazon The following table shows Amazons approximate net sales (revenue) and net income (profit) in the period 2011-2014:68 Net Sales ($ billion) 50 60 70 80 Net Income ($ billion) 0.6 0.1 0.3 0.3 a. Use this information to find a linear regression model for Amazon's net income I (in millions of dollars) as a function of net sales S (in billions of dollars). Plot the data and regression line. b. Give the units of measurement and interpretation of the slope. c. What, according to the model, would Amazon need to earn in net sales for its net income to be $0.5 billion? (Round answer to the nearest billion dollars.) d. Based on the graph, would you say that the linear model is reasonable? Why or why not?Operating Expenses: Amazon The following table shows Amazons approximate net sales (revenue) and operating expenses in 2011-2014:69 Net Sales ($ billion) 50 60 70 80 Operating Expenses ($ billion) 11 16 23 25 a. Use this information to find a linear regression model for Amazon's operating expenses E (in billions of dollars) as a function of net sales S (in billions of dollars). Plot the data and regression line. b. Give the units of measurement and interpretation of the slope. c. What, according to the model, would Amazon need to earn in net sales for its operating expenses to be $5 billion? (Round answer to the nearest billion dollars.) d. Based on the graph, would you say that the linear model is reasonable? Why or why not?23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E New York City Housing Costs at the Turn of the Century The following table shows the average price of a two-bedroom apartment in downtown New York City from 1994 to 2004 (t=0 represents 1994):75 Year t 0 2 4 6 8 10 Price p ($ million) 0.38 0.40 0.60 0.95 1.20 1.60 a. Use technology to obtain the linear regression line and correlation coefficient r, with all coefficients rounded to two decimal places, and plot the regression line and the given points. b. Does the graph suggest that a nonlinear relationship between t and p would be more appropriate than a linear one? Why or why not? c. Use technology to obtain the residuals. What can you say about the residuals in support of the claim in part (b)?Fiber-Optic Connections at the Turn of the Century The following table shows the number of fiber-optic cable connections to homes in the United States from 2000 to 2004 (t=0 represents2000):76 Year t 0 1 2 3 4 Connections c (thousands) 0 10 25 65 150 a. Use technology to obtain the linear regression line and correlation coefficient r, with all coefficients rounded to two decimal places, and plot the regression line and the given points. b. Does the graph suggest that a nonlinear relationship between t and c would be more appropriate than a linear one? Why or why not? c. Use technology to obtain the residuals. What can you say about the residuals in support of the claim in part (b)?37E 38E 39E 40E 41E 42E 43E 44E 45E 46E Sketch the graph of the quadratic functions in Exercises 1 and 2, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). f(x)=x2+2x3 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE In Exercises 15-18, find a formula of the form f(x)=Abx using the given information. f(0)=4.5; the value of triples for every half-unit increase in x.16RE 17RE 18RE 19RE 20RE In Exercises 21-24, use the given information to find an exponential model of the form Q=Q0ekt or Q=Q0ekt, as appropriate. Round all coefficients to three significant digits when rounding is necessary. Q is the amount of radioactive substance with a half-life of 100 years in a sample originally containing 5 grams (t is time in years).In Exercises 21-24, use the given information to find an exponential model of the form Q=Q0ekt or Q=Q0ekt, as appropriate. Round all coefficients to three significant digits when rounding is necessary. Q is the number of cats on an island whose cat population was originally 10,000 but is being cut in half every 5 years (t is time in years).23RE 24RE 25RE In Exercises 25-28, find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $2,000 invested at 6.75%, compounded daily; goal: $3,000 In Exercises 25-28, find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $2,000 invested at 3.75%, compounded continuously; goal: $3,000 In Exercises 25-28, find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $1,000 invested at 100%, compounded quarterly; goal: $1,200 In Exercises 29-32, find an equation for the logistic function of x with the stared properties. Through (0,100), initially increasing by 50% per unit of x, and limiting value 900.In Exercises 29-32, find an equation for the logistic function of x with the stared properties. Initially exponential of the form y=5(1.1)x withlimiting value 25.In Exercises 29-32, find an equation for the logistic function of x with the stared properties. Passing through (0,5) and decreasing from a limiting value of 20 to 0 at a rate of 20% per unit of x when x is near 0.In Exercises 29-32, find an equation for the logistic function of x with the stared properties. Initially exponential of the form y=2(0.8)x witha value close to 10 when x=60.Website Traffic The daily traffic (hits per day) at OHaganBooks.com apparently depends on the monthly expenditure on Internet advertising. The following model is based on information collected over the past few months: h=0.000005c2+0.085c+1,750 Here, h is the average number of bits per day at OHaganBooks.com, and c is the monthly advertising expenditure. a. According to the model, what monthly advertising expenditure will result in the largest volume of traffic at OHaganBooks.com? What is that volume? b. In addition to predicting a maximum volume of traffic, the model predicts that the traffic will eventually drop to zero if the advertising expenditure is increased too far. What expenditure (to the nearest dollar) results in no website traffic? c. What feature of the formula for this quadratic model indicates that it will predict an eventual decline in traffic as advertising expenditure increases?Revenue and Profit Some time ago, a consultant formulated the following linear model of demand for online novels: q=60p+950, where q is the monthly demand for OHaganBooks.coms online novels at a price of p dollars per novel. a. Use this model to express the monthly revenue as a function of the unit price p. Hence, determine the price you should charge for a maximum monthly revenue. b. Author royalties and copyright fees cost the company an average of $4 per novel, and the monthly cost of operating and maintaining the online publishing service amounts to $900 per month. Express the monthly profit P as a function of the unit price p. Hence, determine the unit price you should charge for a maximum monthly profit. What is the resulting profit (or loss)?Revenue and Profit Billy-Sean OHagan is John OHagans son and a freshman in college. He notices that the demand for the college newspaper was 2,000 copies each week when the paper was given away free of charge but dropped to 1,000 each week when the college started charging 10/copy. a. Write down the associated linear demand function. b. Use your demand function to express the revenue as a function of the unit price p. Hence, determine the price the college should charge for a maximum revenue. At that price, what is the revenue from sales of one edition of the newspaper? c. It costs the college 4 to produce each copy of the paper plus an additional fixed cost of $200. Express the profit P as a function of the unit price p. Hence, determine the unit price the college should charge for a maximum monthly profit (or minimum loss). What is the resulting profit (or loss)?Lobsters Marjory Duffin, CEO of Duffin House, is particularly fond of having steamed lobster at working lunches with executives from OHaganBooks.com and is therefore alarmed to learn that the yearly lobster harvest from New Yorks Long Island Sound has been decreasing dramatically since 1997. Indeed, the size of the annual harvest can be approximated by n(t)=9.1(0.81t) millionpounds, where t is time in years since 1997.59 a. The model tells us that the harvest was ______ pounds in 1997 and decreasing by _______% each year. b. What does the model predict for the 2013 harvest?Stock Prices In the period immediately following its initial public offering (IPO), OHaganBooks.com's stock was doubling in value every 3 hours. If you bought $10,000 worth of the stock when it was first offered, how much was your stock worth after 8 hours?39RE 40RE 41RE 42RE 43RE 44RE 45RE 50RE In Exercises 16, (a) state the values of a, b, and c in the given quadratic function f(x)=ax2+bx+c; (b) supply the missing values in the table below; (c) calculate f(a+h); and (d) give a valid technology formula for f(x). (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 13.] x 3 2 1 0 1 2 3 f(x) f(x)=2x2x2 In Exercises 16, (a) state the values of a, b, and c in the given quadratic function f(x)=ax2+bx+c; (b) supply the missing values in the table below; (c) calculate f(a+h); and (d) give a valid technology formula for f(x). (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 13.] x 3 2 1 0 1 2 3 f(x) f(x)=2x2+x+2 In Exercises 16, (a) state the values of a, b, and c in the given quadratic function f(x)=ax2+bx+c; (b) supply the missing values in the table below; (c) calculate f(a+h) ; and (d) give a valid technology formula for f(x). (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 13.] x 3 2 1 0 1 2 3 f(x) f(x)=10x25x In Exercises 16, (a) state the values of a, b, and c in the given quadratic function f(x)=ax2+bx+c; (b) supply the missing values in the table below; (c) calculate f(a+h); and (d) give a valid technology formula for f(x). (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 13.] x 3 2 1 0 1 2 3 f(x) f(x)=x250 In Exercises 16, (a) state the values of a, b, and c in the given quadratic function f(x)=ax2+bx+c; (b) supply the missing values in the table below; (c) calculate f(a+h); and (d) give a valid technology formula for f(x). (Optional: Use technology to check the values in the table.) [HINT: See Quick Examples 13.] x 3 2 1 0 1 2 3 f(x) f(x)=x2x1 6E 7E 8E In Exercises 716, sketch the graph of the quadratic function, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). [HINT: See Example 1.] f(x)=x2+4x4 10E 11E In Exercises 716, sketch the graph of the quadratic function, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). [HINT: See Example 1.] f(x)=x210x600 In Exercises 716, sketch the graph of the quadratic function, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). [HINT: See Example 1.] f(x)=x2+x1 14E 15E 16E In Exercises 1720, for each demand equation, express the total revenue R as a function of the price p per item, sketch the graph of the resulting function, and determine the price p that maximizes total revenue in each case. [HINT: See Example 3.] q=4p+100 18E 19E 20E 21E In Exercises 2124, use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) [HINT: See Example 5.] (1,2),(3,5),(4,3),(5,1)23E In Exercises 2124, use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) [HINT: See Example 5.] (2,5),(3,5),(5,3)World Military Expenditure The following chart shows total military and arms trade expenditure from 19922010 (t=0 represents 1990).2 Source: www.globalissues.org/Geopolitics/ArmsTrade/Spending.asp. a. If you want to model the expenditure figures with a function of the form f(t)=at2+bt+c, would you expect the coefficient a to be positive or negative? Why? [HINT: See Features of a Parabola in this section.] b. Which of the following models best approximates the data given? (Try to answer this without actually computing values.) A. f(t)=4t256t1,300 B. f(t)=4t256t+1,300 C. f(t)=4t256t+1,300 D. f(t)=4t256t1,300 c. What is the nearest year that would correspond to the vertex of the graph of the correct model from part (b)? What is the danger of extrapolating the data in either direction?Education Expenditure The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009. (t=3 represents the start of 2003.) Source: www.globalissues.org/Geopolitics/ArmsTrade/Spending.asp a. If you want to model the percentage figures with a function of the form f(t)=at2+bt+c, would you expect the coefficient a to be positive or negative? Why? [HINT: See Features of a Parabola in this section.] b. Which of the following models best approximates the data given? (Try to answer this without actually computing values.) A. f(t)=0.04t2+0.3t6 B. f(t)=0.04t2+0.3t+6 C. f(t)=0.04t2+0.3t+6 D. f(t)=0.04t2+0.3t6 c. What is the nearest year that would correspond to the vertex of the graph of the correct model from part (b)? What is the danger of extrapolating the data in either direction?Oil Imports from Mexico Crude oil imports to the United States from Mexico for 20092013 could be approximated by I(t)=39t2+800t3,000 thousand barrels per day (9t13) where t is time in years since the start of 2000.3 According to the model, approximately when were oil imports to the United States greatest? How many barrels per day were imported at that time? (Round the answer to two significant digits.) [HINT: See Example 1.]Oil Production in Mexico Crude oil production by Pemex, Mexicos national oil company, for 20082013 could be approximated by P(t)=0.017t20.4t+5.23 million barrels per day (8t13) where t is time in years since the start of 2000.4 According to the model, approximately when was oil production by Pemex least? What was the oil production at that time? (Round the answer to two significant digits.) [HINT: See Example 1.]GE Net Income 20092013 The annual net income of General Electric for the period 20092013 could be approx- imated by P(t)=0.39t2+5.2t4.1 billion dollars (4t8), where t is time in years since the start of 2005.5 According to the model, during what year in this period was General Electrics net income highest? What was the corresponding net income? Would you trust this model to continue to be valid long past this period? Why or why not?GE Net Income 20072011 The annual net income of General Electric for the period 20072011 could be approximated by P(t)=1.6t215t+46 billion dollars (2t6), where t is time in years since the start of 2005.6 According to the model, during what year in this period was General Electrics net income lowest? What was the corresponding net income? Would you trust this model to continue to be valid long past this period? Why or why not?Revenue The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q=0.5p+140, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue? [HINT: See Example 3.]32E Revenue Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, because of the crowding and smaller lot sizes. In fact, if it builds 40 houses in this particular development, it can sell them for $200,000 each, but if it builds 60 houses, it will be able to get only $160,000 each. Obtain a linear demand equation, and hence determine how many houses Pack-Em-In should build to get the largest revenue. What is the largest possible revenue? [HINT: See Example 3.]Revenue Pack-Em-In has another development in the works. If it builds 50 houses in this development, it will be able to sell them at $190,000 each, but if it builds 70 houses, it will get only $170,000 each. Obtain a linear demand equation, and hence determine how many houses it should build to get the largest revenue. What is the largest possible revenue?Revenue from Monorail Service, Las Vegas In 2005 the Las Vegas monorail charged $3 per ride and had an average ridership of about 28,000 per day. In December 2005 the Las Vegas Monorail Company raised the fare to $5 per ride, and average ridership in 2006 plunged to around 19,000 per day.7 a. Use the given information to find a linear demand equation. b. Find the price the company should have charged to maximize revenue from ridership. What is the corresponding daily revenue? c. The Las Vegas Monorail Company would have needed $44.9 million in revenues from ridership to break even in 2006. Would it have been possible to break even in 2006 by charging a suitable price?Revenue from Monorail Service, Mars The Utarek monorail, which links the three urbynes (or districts) of Utarek on Mars, charged Z5 per ride8 and sold about 14 million rides per day. When the Utarek City Council lowered the fare to Z3 per ride, the number of rides increased to 18 million per day. a. Use the given information to find a linear demand equation. b. Find the price the City Council should have charged to maximize revenue from ridership. What is the corresponding daily revenue? c. The City Council would have needed to raise Z48 billion in revenues from ridership each Martian year (670 days9) to finance the new Mars organism research lab. Would this have been possible by charging a suitable price?Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $2, the demand was 280 log-ons per month. When you lowered the price to $1.50, the demand increased to 560 log-ons per month. a. Construct a linear demand function for your website and hence obtain the monthly revenue R as a function of the log-on fee x. b. Your Internet provider charges you a monthly fee of $30 to maintain your site. Express your monthly profit P as a function of the log-on fee x, and hence determine the log-on fee you should charge to obtain the largest possible monthly profit. What is the largest possible monthly profit? [HINT: See Example 4.]T-Shirt Profit Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 400 shirts in a week at $8 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 600 per week at $4 per shirt. a. On the basis of this information, construct a linear demand equation for Yoda vs. Alien T-shirts. Hence, obtain the weekly revenue R as a function of the unit price x. b. The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the monthly profit P as a function of the unit price x. Hence, determine how much the fraternities should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit? [HINT: See Example 4.]Website Profit The latest demand equation for your gaming website, www.mudbeast.net, is given by q=400x+1,200 where q is the number of users who log on per month and x is the log-on fee you charge. Your Internet provider bills you as follows: Site maintenance fee: $20 per month High-volume access fee: 50 perlog-on Find the monthly cost as a function of the log-on fee x. Hence, find the monthly profit as a function of x, and determine the log-on fee you should charge to obtain the largest possible monthly profit. What is the largest possible monthly profit?T-Shirt Profit The latest demand equation for your Yoda vs. Alien T-shirts is given by q=40x+600, where q is the number of shirts you can sell in one week if you charge $x per shirt. The Student Council charges you $400 per week for use of their facilities, and the T-shirts cost you $5 each. Find the weekly cost as a function of the unit price x. Hence, find the weekly profit as a function of x, and determine the unit price you should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit?Nightclub Management You have just opened a new nightclub, Russ Techno Pitstop, but are unsure how high to set the cover charge (entrance fee). One week you charged $10 per guest and averaged 300 guests per night. The next week you charged $15 per guest and averaged 250 guests per night. a. Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. b. Find the nightly revenue R as a function of the cover charge p. c. The club will provide two free nonalcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $3,000. Find the cost C as a function of the cover charge p. d. Now find the profit in terms of the cover charge p. Hence, determine the entrance fee you should charge for a maximum profit.Television Advertising As sales manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 15 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,000. a. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Monte-video charges for development. b. On average, Montevideo bills for 50 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour. c. The costs to Montevideo Productions are estimated as follows: Fixed costs: $120,000 per month Variable costs: $80,000 per contract Express Montevideo Productions monthly cost (i) as a function of the number q of contracts and (ii) as a function of the hourly production charge p. d. Express Montevideo Productions monthly profit as a function of the hourly development fee p. Hence, find the price it should charge to maximize the profit.43E 44E iPod Sales The following table shows Apple iPod sales during the financial years 20102014. (t is time in years since 2010.)12 Year t 0 1 2 3 4 iPod Sales (millions) 50.4 42.6 35.2 26.4 14.4 a. Find a quadratic regression model for these data. (Round coefficients to two significant digits.) Graph the model together with the data. b. What does the model predict for iPod sales in 2015 and 2016, to the nearest million? Comment on the answers.iPod Sales The following table shows Apple iPod sales during the financial years 20052009. (t is time in years since 2005.)13 Year t 0 1 2 3 4 iPod Sales (millions) 22.5 39.4 51.6 54.8 54.1 a. Find a quadratic regression model for these data. (Round coefficients to two significant digits.) Graph the model together with the data. b. What does the model predict for iPod sales in 2010 and 2011, to the nearest million? Comment on the answers.What can you say about the graph of f(x)=ax2+bx+c if a=0?48E Multiple choice: Following is the graph of f(x)=ax2+bx+c; (A) a is positive and c is positive. (B) a is negative and c is positive. (C) a is positive and c is negative. (D) a is negative and c is negative.50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E If the revenue function for a particular commodity is R(p)=50p2+60p, what is the (linear) demand function? Give a reason for your answer.If the revenue function for a particular commodity is R(p)=50p2+60p+50, can the demand function be linear? What is the associated demand function?In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) f(x)=4x In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) f(x)=3x In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) f(x)=3x 4E 5E In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) g(x)=2(3x)7E 8E 9E 10E In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) s(x)=2x1 12E In Exercises 13-18, graph the given function using a chart of values. (Use 3x3.) f(x)=3x 14E 15E In Exercises 13-18, graph the given function using a chart of values. (Use 3x3.) g(x)=2(3x)17E In Exercises 13-18, graph the given function using a chart of values. (Use 3x3.) h(x)=2(3x)In Exercises 19-24 the values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Decide which, if any, are exponential, and give the exponential models for those that are. [HINT: See Example 1.] x 2 1 0 1 2 f(x) 0.5 1.5 4.5 13.5 40.5 g(x) 8 4 2 1 12 20E 21E 22E 23E 24E In Exercises 25-30, supply a valid technology formula for the given function, and then use technology to compute the missing values in the following table accurate to four decimal places. [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) f(x)=e2x 26E 27E 28E In Exercises 25-30, supply a valid technology formula for the given function, and then use technology to compute the missing values in the following table accurate to four decimal places. [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) r(x)=50(1+13.2)2x In Exercises 25-30, supply a valid technology formula for the given function, and then use technology to compute the missing values in the following table accurate to four decimal places. [HINT: See Quick Examples 1-4.] x 3 2 1 0 1 2 3 f(x) r(x)=0.043(4.551.2)x 31E 32E 33E

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