From Gravity and Levity:
What do you think are the odds that you will die during the next year? Try to put a number to it — 1 in 100? 1 in 10,000? Whatever it is, it will be twice as large 8 years from now.
This startling fact was first noticed by the British actuary Benjamin Gompertz in 1825 and is now called the “Gompertz Law of human mortality.” Your probability of dying during a given year doubles every 8 years. For me, a 25-year-old American, the probability of dying during the next year is a fairly minuscule 0.03% — about 1 in 3,000. When I’m 33 it will be about 1 in 1,500, when I’m 42 it will be about 1 in 750, and so on. By the time I reach age 100 (and I do plan on it) the probability of living to 101 will only be about 50%. This is seriously fast growth — my mortality rate is increasing exponentially with age.
And if my mortality rate (the probability of dying during the next year, or during the next second, however you want to phrase it) is rising exponentially, that means that the probability of me surviving to a particular age is falling super-exponentially. Below are some statistics for mortality rates in the United States in 2005, as reported by the US Census Bureau (and displayed by Wolfram Alpha):
This data fits the Gompertz law almost perfectly, with death rates doubling every 8 years. The graph on the right also agrees with the Gompertz law, and you can see the precipitous fall in survival rates starting at age 80 or so.
More here.