Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Sales Income The following table shows the net monthly income
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a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in
b. Use the average rate of change to estimate the net monthly income for monthly real estate sales of
c. Would you expect
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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- 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_forwardImmigration The following graph shows immigrationin thousand to the United States has varied over the past century. Source: Homeland Security. a. Find the average annual rate of change in immigration for the first half of the century from 1905 to 1955. b. Find the average annual rate of change in immigration for the second half of the century from 1955 to 2005. c. Find the average annual rate of change in immigration for the entire century from 1905 to 2005. d. Average your answers to part a and b, and compare the result with your answer from part c. Will these always be equal for any two time periods? e. If the annual average rate of change for entire century continues, predict the number of immigrants in 2009. Compare answer to the actual number of 1,130,818 immigrants.arrow_forwardLIFE SCIENCE APPLICATIONS Brain Mass The brain mass of a fetus can be estimated using the total mass of the fetus by the function b=0.22m0.87, where m is the mass of the fetus in grams and b is the brain mass in grams. Suppose the brain mass of a 25-g fetus is changing at a rate of 0.25gperday. Use this to estimate the rate of change of the total mass of the fetus, dm/dt. Source: Archives dAnatomie, d Histologie et d Embryologie.arrow_forward
- Mass of Bighorn Yearlings The body mass of yearling bighorn sheep on Ram Mountain in Alberta, Canada, can be estimated by M(t)=27.5+0.3t0.001t2 Where M(t) is measured in kilograms and t is days since May 25. Source: Canadian Journal of zoology. a. Find the average rate of change of the mass of bighorn yearling between 105 and 115 days past May 25. b. Find the instantaneous rate of change of the mass for a bighorn yearling sheep whose age is 105 days past May 25. c. Graph the function M(t) on [5,125] by [25,65]. d. Does the behavior of the function past 125 days accurately model the mass of the sheep? Why or why not? e. f. g.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_forwardRound all answers to two decimal places unless otherwise indicated. 24. Timber Stumpage Price The following table shows timber stumpage prices for pine pulpwood in two regions of the American South. Prices are in dollars per ton and were recorded at the start of the indicated year. Year Southeast Mid-Atlantic 2002 6.50 4.00 2005 7.50 6.70 2007 7.00 10.00 a. For the Mid-Atlantic, what is the average rate of change per year in price from 2002 to 2005? b. Use your answers to part a to estimate the price in the Mid-Atlantic region at the start of 2004. The actual price was 6.40 per ton. c. For the southeast, what is the average rate of change per year in price form 2005 to 2007? d. Use your answer to part c to estimate the price in the Southeast at the start of 2008. e. For each region, find the percentage increase in price from 2002 to 2007. f. On the basis of your answer to part e, in the absence of other factors, would an investor in timber be better advised to choose the Southeast or the Mid-Atlantic?arrow_forward
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