Adjusted Gross Income An individual’s adjusted gross income is the amount of income that is subject to federal income tax. The following table shows the total adjusted gross income (AGI), in trillions of dollars, reported to the IRS in the given year.
Year | 2009 | 2010 | 2011 | 2012 |
AGI (trillions) | 7.6 | 8.1 | 8.6 | 9.1 |
a. Show that the data are linear.
b. Let t denote the time in years since 2009, and let A denote the total adjusted gross income. Find a linear model for A as a function of t.
c. Identify the slope of the linear model you found in part b, and explain its meaning in practical terms.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Webassign Printed Access Card For Crauder/evans/noell's Functions And Change: A Modeling Approach To College Algebra, 6th Edition, Single-term
Additional Math Textbook Solutions
Elementary Algebra: Concepts and Applications (10th Edition)
Algebra And Trigonometry (11th Edition)
Elementary Linear Algebra (Classic Version) (2nd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Beginning and Intermediate Algebra (6th Edition)
Elementary Algebra For College Students (10th Edition)
- Mortgage 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_forwardMarginal Tax Rate The following table shows tax due for the given taxable income level for a single taxpayer. Taxable income Tax due 97, 000 21, 913 97, 050 21, 927 97, 100 21, 941 97, 150 21, 955 97, 200 21, 969 a. Show that the data in the table are linear. b. How much additional tax is due on each dollar over 97.000? c. What would you expect to be your tax due if you had a taxable income of 97, 000? of 98, 000? d. Find a linear formula that gives your tax due if your income is A dollars over 97, 000.arrow_forwardDVD 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_forward
- Table 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?arrow_forwardTable 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?arrow_forwardDepreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forward
- Using the model in Example 6, estimate the number of cases of flu on day 15.arrow_forward6. Tuition at American Private Universities The following table shows the average yearly tuition and required fees, in dollars, charged by four-year American private nonprofit universities in the school year ending in the given year. Date Average tuition 2012 27,870 2013 29,004 2014 30,138 2015 31,272 2016 32,406 a. Show that these data can be modeled by a linear function, and find its formula. b. Plot the data points and add the graph of the linear formula you found in part a. c. What prediction does this formula give for average tuition and fees at four-year American private nonprofit universities for the academic year ending in 2021?arrow_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning