Concept explainers
In Example 1 on page 520, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points to solve Exercises 66–70.
66.
- a. Use your graphing utility’s exponential regression option to obtain a model of the form y = abx that fits the data. How well does the
correlation coefficient , r, indicate that the model fits the data? - b. Rewrite the model in terms of base e. By what percentage is the population of the United States increasing each year?
67. Use your graphing utility’s logarithmic regression option to obtain a model of the form y = a + b ln x that fits the data. How well does the correlation coefficient, r, indicate that the model fits the data?
68. Use your graphing utility’s linear regression option to obtain a model of the form y = ax + b that fits the data. How well does the correlation coefficient, r, indicate that the model fits the data?
69. Use your graphing utility’s power regression option to obtain a model of the form y = axb that fits the data. How well does the correlation coefficient, r, indicate that the model fits the data?
70. Use the values of r in Exercises 66–69 to select the two models of best fit. Use each of these models to predict by which year the U.S. population will reach 335 million. How do these answers compare to the year we found in Example 1, namely 2020? If you obtained different years, how do you account for this difference?
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College Algebra Essentials
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