Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Averages and Average Rate of Change The following is a partial table of values for
|
|
|
|
|
|
|
|
|
|
a. Estimate the value of
b. Find the average rate of change for
Want to see the full answer?
Check out a sample textbook solutionChapter 1 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
EBK ALGEBRA FOUNDATIONS
Pre-Algebra Student Edition
Algebra and Trigonometry
Elementary Algebra
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
College Algebra (5th Edition)
- The 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_forwardRate of Change for a Linear Function If f is the linear function f=45x, what is the value of dfdx?arrow_forwardFarms 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_forward
- For the experimental can described in Example 8, write the surface area as a function of (a) the radius r and (b) the height h.arrow_forwardA Mathematical Term: If f=f(x), then we use dfdx to denote the rate of change in f. What is the technical mathematical term for dfdx?arrow_forwardPopulation Growth and Decline The graph shows the population P in a small industrial city from 1950 to 2000. The variable x represents the number of years since 1950. (a) What was the average rate of change of P between x=20 and x=40 ? (b) Interpret the value of the average rate of change that you found in part (a).arrow_forward
- Run from Slope and Rise Suppose that f is a linear function with slope 3.4 and that f(1)6. What value of x gives f(x)=0?arrow_forwardWhen Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12arrow_forwardResearch and Development The amounts (in billions of dollars) the U.S. federal government spent on research and development for defense from 2010 through 2014 can be approximated by the model y=0.5079t28.168t+95.08 where t represents the year, with t=0 corresponding to 2010. (a) Use a graphing utility to graph the model. (b) Find the average rate of change of the model from 2010 to 2014. Interpret your answer in the context of the problem.arrow_forward
- Printing Cost A publisher estimates that the cost C(x) of printing a run of x copies of a certain mathematics textbook is given by the function C(x)=5000+30x0.001x2 . (a) Find C(1000) and C(10,000) . (b) What do your answer in part (a) represent? (c) Find C(0) . What does this number represent? (d) Find the net change and the average rate of change of the cost C between x=1000 and x=10,000 .arrow_forwardPopulation Growth and Decline The table gives the population in a small coastal community for the period 1997-2006. Figures shown arc for January 1 in each year. (a) What was the average rate of change of population between 1998 and 2001? (b) What was the average rate of change of population between 2002 and 2004? (C) For what period of lime was the population increasing? (d) For what period of time was the population decreasing?arrow_forwardDVD Player sales The table shows the number of DVD play-ers sold in a small electronics store in the years 2003-2013. What was the average rate of change of sales between 2003 and 2013? Whatwas the average rate of change of sales between 2003 and 2004? What was the average rate of change of sales between 2004 and 2005? Between which two successive years did DVD player sales increase most quickly?arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- 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 HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage