"Growth" here refers to the size of the installed user base, irrespective of retention. By "self-sustaining" I mean it requires no external input of users to c

"Growth" here refers to the size of the installed user base, irrespective of retention. By "self-sustaining" I mean it requires no external input of users to continue to grow. Using your model, let's say usersLosingInterest = 0 and 0 < viralCoefficient < 1. How do you get exponential growth from this? Each new user brings in a finite number of additional users, a function of viralCoefficient. Call this number N. This increases your growth by a factor of N, but it's still dependent on some outside source of users. If I acquire M users then through my viral process I get an additional M*N users total. Another way to think about it: if your viral coefficient is less than one then the viral growth of each cohort dies out. I see nothing exponential here. Am I missing something? This point is mostly incidental to my two main points, though: outlining how the viral coefficient affects the cost of acquisition, and an argument for a hybrid strategy of accelerated but not viral growth. What do you think of those points?