Why does the risk of dying roughly double every eight years of adult life?

Because adult mortality grows almost exponentially: the yearly chance of dying approximately doubles every eight years of age. This pattern is known as the Gompertz law, after the English actuary Benjamin Gompertz, who proposed in 1825 that the age-specific force of mortality increases approximately exponentially with age. After early adulthood, many populations follow it reasonably well.

Doubling sounds modest, but it compounds. If the risk at 30 is one unit, eight years later it is two, at 46 it is four, at 54 eight, and so on. Over a few decades the risk climbs steeply, which is why the same law that makes a 30-year-old's death rare makes an 80-year-old's death common. On a graph with a logarithmic axis, this shows up as an almost straight line across adult life, a visual check demographers use.

Gompertz was an unlikely founder of demography. Barred as a Jew from a university education, he studied on his own, and tables of mortality that he worked out for the Royal Society suggested his law to him. In 1860 William Makeham added a roughly age-independent term for deaths from external causes that affect all ages, giving the Gompertz–Makeham law.

Treat the eight years as a rule of thumb. The exact rate varies somewhat between populations, sexes and historical periods. The model is not meant to describe the high mortality of infancy and early childhood, and at the very highest ages the estimates are sensitive to data quality and modelling assumptions.