Expert: Scott A Wilson - 8/30/2011

Question
The average life expectancy increased linearly from 62.9 years for a person born in 1940, to 75.4 years for a person born in 1990.

a) Write the equation for life expectancy of a person born in year x, for x=0 corresponding to 1940.

b) Will this equation likely remain accurate in years to come? Explain.  (---just need to know how to tell if it will---)

Answer
a) If year 1940 is when x = 0, then in 1990, x = 1990 - 1940 = 50.
The change in y is 75.4 - 62.9 = 12.5.
Since the increase each year is then 12.5/50, that gives 0.25 per year.

This means the equation is y = 0.25x + 62.9.

b) Using this for the estimate just a few years in the future or in the past would probably hold,
but over a long time, it would not.  This can be seen by seeing what, according to this equation, the life expectancy was 1,000 years ago.  The equation would say y = -250 + 62.9.
That would be -187.1, and that makes no sense.  This would imply that the equation was not truly linear and there would be no reason to believe it would become linear in the future.