(Chapter Opener Revisted) In the discussion that introduced this chapter, we looked at a plot that displayed how the center of population (measured to the nearest degree of west longitude) of the United States moved west over the years 1820 to 1940. The plot was based on the data in the following table.
Year | 1820 | 1860 | 1900 | 1940 |
west longitude (degrees) | 79 | 83 | 86 | 87 |
a. Find the best-fitting logarithmic model for these data, with t = 0 in 1800.
b. Use your model to predict the west longitude of the center of population in 1950.
c. From 1950 onward, Alaska and Hawaii are included in the calculation of the center. In 1950 the actual center of population was at a longitude of 88 degrees. How does your prediction from part (b) compare to this value?
d. The following table gives the center of the U.S. population for years beginning in 1950.
Year
1950
1970
1980
2000
west longitude (degrees)
88
89
90
91
Make a scatter plot of these data, and use it to determine whether a linear, exponential, or logarithmic model is best suited to fit the data. Then find the best-fitting model of that type.
e. Use your model to predict the year in which the center of population will be at 95 degrees.
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