Gompertz law

Gompertz law, formulated by the British actuary Benjamin Gompertz in 1825, describes the empirical observation that human mortality risk increases exponentially with adult age: specifically, the force of mortality (hazard rate) approximately doubles every 8 years in most high-income populations. Mathematically, the instantaneous mortality rate is expressed as μ(t) = a·e^(bt), where a is the baseline mortality rate and b is the age-dependent acceleration. The law holds across most of adult life in humans and many other species, but mortality deceleration or plateaus observed at very old ages suggest it is not universal beyond the oldest cohorts. Gompertz dynamics are central to actuarial science, epidemiology, and the theoretical biology of ageing.