  In exponential population growth, variability in the timing of individual
division events and environmental factors (including stochastic inoculation)
compound to produce variable growth trajectories. In several stochastic models
of exponential growth we show power-law relationships that relate variability
in the time required to reach a threshold population size to growth rate and
inoculum size. Population-growth experiments in E. coli and S. aureus with
inoculum sizes ranging between 1 and 100 are consistent with these
relationships. We quantify how noise accumulates over time, finding that it
encodes -- and can be used to deduce -- information about the early growth rate
of a population.
