Population The populations y (in millions) of the United

Chapter 3, Problem 3.6.29

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Population The populations y (in millions) of the United States for the years 1991 through 2004 are shown in the table, where t represents the year, with corresponding to 1991. (Source: U.S. Census Bureau) (a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (b) Use the regression feature of a graphing utility to find a power model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (c) Use the regression feature of a graphing utility to find an exponential model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (d) Use the regression feature of a graphing utility to find a quadratic model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (e) Which model is the best fit for the data? Explain. (f) Use each model to predict the populations of the United States for the years 2005 through 2010. (g) Which model is the best choice for predicting the future population of the United States? Explain. (h) Were your choices of models the same for parts (e) and (g)? If not, explain why your choices were different.