Concept explainers
Gross Domestic Product The following table shows the U.S gross domestic product (GDP)
|
|
|
|
|
|
|
|
a. Explain in practical terms what
b. Use functional notation to express the gross domestic product in
c. What is the average yearly rate of change in
d. Use your answer to part c to predict the gross domestic product in the year
Trending nowThis is a popular solution!
Chapter 1 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra (Collegiate Math)
Elementary & Intermediate Algebra
Precalculus: A Unit Circle Approach (3rd Edition)
Elementary Statistics
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Intro Stats, Books a la Carte Edition (5th Edition)
- Weight Versus Height The following data show the height h, in inches, and weight w, in pounds, of an average adult male. h 61 62 66 68 70 72 74 75 w 131 133 143 149 155 162 170 175 a Make a power model for weight versus height. b According to the model from part a, what percentage increase in weight can be expected if height is increased by 10?arrow_forwardStopping Distance The table below shows the average stopping distance D, in feet, for a car on dry pavement versus the speed S of the car, in miles per hour. S= speed mph 15 25 35 40 60 75 D = stopping distance feet 44 85 136 164 304 433 a Find a model of stopping distance as power function of speed. b If speed is doubled, how is stopping distance affected? c Plot the data and the power model on the same screen.arrow_forwardHydroplaning On wet roads, under certain conditions the front tires of a car will hydroplane, or run along the surface of the water. The critical speed V at which hydroplaning occurs is a function of p, the tire inflation pressure. The following table shows hypothetical data for p, in pounds per square inch, and V, in miles per hour. Tire inflation pressure p Critical speed V for hydroplaning 20 46.3 25 51.8 30 56.7 35 61.2 a Find a formula that models V as a power function of p. b In the rain, a car with tires inflated to 35pound per square inch is travelling behind a bus with tires inflated to 60 pounds per square inch, and both are moving at 65 miles per hour. If they both hit their brakes, what might happen?arrow_forward
- DVD Player Sales The table shows the number of DVD players sold in a small electronics store in the years 2003-2013. Year DVD players sold 2003 495 2004 513 2005 410 2006 402 2007 520 2008 580 2009 631 2010 719 2011 624 2012 582 2013 635 aWhat was the average rate of change of sales between 2003 and 2013? bWhat was the average rate of change of sales between 2003 and 2004? cWhat was the average rate of change of sales between 2004 and 2005? dBetween which two successive years did DVD player sales increase most quickly? Decrease most quickly?arrow_forwardThe American Food Dollar The following table shows the percentage P=P(d) of the American food dollar that was spent on eating away from home at restaurants, for example as function of the date d. d=Year P=Precentspentawayfromhome 1969 25 1989 30 2009 34 a. Find P(1989) and explain what it means. b. What does P(1999) mean? Estimate its value. c. What is the average rate of change per year in percentage of the food dollar spent away from home for the period from 1989 to 2009? d. What does P(2004) mean? Estimate its value. Hint: Your calculation in part c should be useful. e. Predict the value of P(2014) and explain how you made your estimate.arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forward
- Farms in the United States The graph gives the number of farms in the United States from 1850 to 2000. aEstimate the average rate of change in the number of farms between i 1860 and 1890 and ii 1950 and 1970. bIn which decade did the number of farms experience the greatest average rate of decline?arrow_forwardMortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forwardFreight on Class I Railroads According to the Association of American Railroads, Class I freight railroads are the line-haul freight railroads with 2006 operating revenue in excess of 346.8million. Let F=F(t) denote the freight revenue in billions of dollars of Class I railroads in year t. In 2005, Class I railroads had a freight revenue of 44.5billion. In 2007, the revenue was 52.9 billion. Calculate the average rate of change per year in F from 2005 to 2007 and explain its meaning in practical terms.arrow_forward
- World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forwardMonth September October November KWPH 115 151 164 Consumption (K) Amount Due 1,216.85 1,697.22 1,903.84 Based on the table, what is the constant variation (K)?arrow_forwardAdvanced Matharrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning