I'm a bit confused about exp growth and exp distribution. Suppose I have a branching process situation, where there are n individuals in generation 0, and each individual produces a random number of offspring, according to some distribution (say Poisson), at each generation. Now, then after a certain number of generations, say generation n+1, the number of copies an individual leaves behind will be either 0 or exponentially distributed. What I don't understand is how the number of copies will be exponentially distributed. I understand that if each an individual leaves more than 1 offspring in each generation then there will be exponential growth for that particular type of individual, but isn't exponential growth different from the exponential distribution. From my understanding an exponential distribution gives the distribution of the time until a certain event occurs, with rate "lamda". So in the situation described above what is this "event", and what should "lamda" be?? So basically I'm trying to understand, how does the exponential distribution model the number of offspring left by an individual??