I agree with @gung 's comment a lot. It is a case of survival analysis. If you have an subject, that you followed for 100hrs without seeing the 'event', it can be treated as a right-censored. If you have an obs. for which the 'event' time is observed at 99 hours, then it is a exact time-event. If you have multiple events observed for one subject, it becomes a repeated event or Recurrent event survival analysis. You can have a subjects tracked for only 10 hours (without seeing an event), then it is right censored at 10hrs. You can have subjects that were tracked for different amount of time.

Sure, this question is regarding the logistic growth model, used mainly in ecology, microbiology and medical research. The model is better illustrated in a form of differential equation: $\frac{df(t)}{dt}=r f(t)(1-\frac{f(t)}{K})$, $r$ is often called intrinsic growth rate and $K$ called carrying capacity, $f(t)$ is the population size/number of animal/bacterial/new product sold at time $t$. $f'(0)$ is the grown rate at zero time also labeled as $R_0$, or I hope that's what the OP means. It couldn't be $r$ for sure.