Solved: Population Statistics The table shows the life expectancies of a child (at

Chapter 1, Problem 87

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Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1930 through 2000. (Source: U.S. National Center for Health Statistics) A model for the life expectancy during this period is where represents the life expectancy and is the time in years, with corresponding to 1930. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 76.0. Verify your answer algebraically. (d) One projection for the life expectancy of a child born in 2015 is 78.9. How does this compare with the projection given by the model? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain.