Formation of bacterial colonies in successive time intervals

By enumerating colonies on a plate in successive equal short intervals of time, we found that the number of colonies formed in individual intervals varied at random and their distribution was approximated by a Poisson series. Based on the result, we derived the equation of colony formation (CF equation). This equation describes the relationship between the cumulative number of colonies and incubation time: N(t) = N infinity (1 - exp[-lambda(t - tr)]) where N(t) is the number of colonies at time t. N infinity, lambda, and tr are parameters, expressing the expected number of colonies on a plate at infinite incubation time, the probability of the occurrence of colony formation in a unit of time, and a retardation time, respectively.