Chapter 1.2, Problem 85E

Skills and Applications

Population Statistics

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)

Year	Life Expectancy, $\mathit{y}$
1940	62.9
1950	68.2
1960	69.7
1970	70.8
1980	73.7
1990	75.4
2000	76.8
2010	78.7

The model for the life expectancy during this period is $y=\frac{63.6+0.97t}{1+0.01t}$, $0\le t\le 70$

where $y$ represents the life expectancy that $t$ 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) Find 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.