Natural selection is thought to shape the evolution of aging patterns, although how life-history trajectories orchestrate the inherently stochastic processes associated with aging is unclear. Tracking clonal growth-arrested Escherichia coli cohorts in an homogeneous environment at single-cell resolution, we demonstrate that the Gompertz law of exponential mortality characterizes bacterial lifespan distributions. By disentangling the rate of aging from age-independent components of longevity, we find that increasing cellular maintenance through the general stress pathway reduces the aging rate and rescales the lifespan distribution at the expense of growth. This trade-off between aging and growth underpins the evolutionary tuning of the general stress response pathway in adaptation to the organism's feast-or-famine lifestyle. It is thus necessary to involve both natural selection and stochastic physiology to explain aging patterns.