The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. (Source: U.S. National Center for Health Statistics)

A model for the life expectancy during this period is y = (63.6 + 0.97t) / (1 + 0.01t), 0 ‰¤ t ‰¤ 70 where y represents the life expectancy and t is the time in years, with t = 0 corresponding to 1940.
(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 70.1. Verify your answer algebraically.
(d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem?
(e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain.

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DATA Year Life Expectancy, y 1940 62.9 1950 68.2 1960 69.7 1970 70.8 1980 73.7 1990 75.4 2000 76.8 2010 78.7 Spreadshe et at LarsonPrecal culus.com