Population Statistics The table shows the life expectancies of a child (at birth) in the U...

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

y = −0.002t2 + 0.50t + 46.6, 30 ≤ t ≤ 100

where y represents the life expectancy and t is the time in years, with t = 30 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.

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(b) Determine the life expectancy in 1990 both graphically and algebraically.

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(c) Use the graph to determine the year when life expectancy was approximately 76.0. Verify your answer algebraically.

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(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?

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(e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain.