Growth in the economy The graph in the accompanying figureshows the average annual percentage change y = f(t) in the U.S.gross national product (GNP) for the years 2005–2011. Graphdy/dt (where defined).7%54322005 2006 2007 2008 2009 2010 2011

Answered: Image /qna-images/answer/3a202f5c-1d7f-4c85-8614-c87d6ba98512.jpg

Answered: Growth in the economy The graph in the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 31E

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Population 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).
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Speed Skating Two speed skaters, A and B, are racing in a 500-m event. The graph shows the distance they have traveled as a function of the time from the start of the race. aWho won the race? bFind the average speed during the first 10 s for each skater. cFind the average speed during the last 15 s for each skater.
A Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?
Population 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?
Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0t70 Where y represents the life expectancy and t is the time in years, with t = 0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. verify your answer algebraically. (d) Find the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now?

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Growth in the economy The graph in the accompanying figure shows the average annual percentage change y = f(t) in the U.S. gross national product (GNP) for the years 2005–2011. Graph dy/dt (where defined). 7% 5 4 3 2 2005 2006 2007 2008 2009 2010 2011