3 ms·
Let C be the original number of companies (or their billings, doesn't matter.) In month 1, we have 1 * C companies. In month 2, we have 1 * .978 * C companies.
by patio11 13y ago
Let C be the original number of companies (or their billings, doesn't matter.)
In month 1, we have 1 * C companies.
In month 2, we have 1 * .978 * C companies. .978 is the survivorship rate, which is the inverse of the churn.
In month 3, we have 1 * .978 * .978 * C companies.
Given that we are most keenly interested in how many company-months we rack up over time, we can solve for this with sum of an infinite geometric series. The formula is C / (1 - s) for s is the survivorship rate, or C / (churn).
Exactly like Gail said it was.
- graphene 13y agothe survivorship rate, which is the inverse of the churn That's an odd definition of survivorship rate though, isn't it? Suppose churn is 75%, that would give a SR of 1.333, which doesn't make sense to me... More logical I think would be SR = (1-churn). Of course, .978 is close enough to 1.0 that it doesn't matter, and I don't understand how the grandparent arrived at 32 months. Edit: your two formulas for total company-months also imply that sr = (1-churn), so maybe I'm missing something?
- mechanical_fish 13y agoSurvivorship = (1 - churn) With this definition, a churn of 0.75 is a survivorship of 0.25. You're perhaps being misled by the offhand phrase "the survivorship is the inverse of the churn"; in that sentence "inverse" is not being used in the mathematician's strict sense of "reciprocal", but in the more colloquial sense of "a thing that moves in the opposite direction from the previous thing". None of us understand where 32 months came from.
- graphene 13y agoAh, that makes sense, thanks, in my mother tounge there's no specific word for "reciprocal", we just use "inverse" for both meanings.