Chapter 1.1, Problem 73E

Life Expectancy Some scientists believe that there is a limit to how long humans can live. One supporting argument is that during the past century, life expectancy from age $65$ has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In $1900$, life expectancy at birth was $46$ yr, and life expectancy at age $65$ was $76$ yr. In $2008$, these figures had risen to $78.1$ and $83.8$, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans. Source: Science.