By using Social Security Administration data for selected years from 1950 and projected to 2050, the additional years of life expectancy at age 65 can be modeled by
L(y) = - 14.6 + 7.10 ln y
where y equals the number of years past 1950.
(a) Find the function that models the rate of change of the years of life expectancy past age 65.
(b) Find and interpret L(50) and L(80).
(c) Find and interpret L'(50) and L'(80).