Concept explainers
Urban World Population Let
denotes the percentage of the world population that is urban
years after
percent of the world's population was urban in
is a linear function of
since
Determine
as a function of
Interpret the slope as a rate of change.
Find the percentage of the world's population that is urban in
Determine the year in which
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- When 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_forwardHigh School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardManufacturing Cost The manager of a furniture factory finds that it costs 2200 to produce 100 chairs in one day and 4800 to produce 300 chairs in one day. a Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x chairs in one day. b Draw a graph of C. What is the slope of this line? c At what rate does the factorys cost increase for every additional chair produced?arrow_forward
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