According to recent data from the Teachers Insurance and Annuity Association (TIAA), the survival function for life after 65 is approximately given by S(x) = 1 - 0.058x - 0.076x², where x is measured in decades. This function gives the probability that an individual who reaches the age of 65 will live at least x decades (10x years) longer. Source: Ralph DeMarr.
(a) Find the median length of life for people who reach 65, that is, the age for which the survival rate is 0.50.
(b) Find the age beyond which virtually nobody lives. (There are, of course, exceptions.)