undefined | Better HN

0 pointsthaumasiotes10mo ago0 comments

> You can see it on revenue as well, since even if growth is exponential, churn is a percentage of your total paying users. Thus, it produces a sigmoid curve unless you can get churn to 0% (pro-tip: you can’t).

Exponential growth means that additional users are a percentage of your total users.

It is trivial to see that adding a source of exponential decay will give you another exponential function. All churn (as you've defined it) does is lower the exponent. It will never take you from exponential to sigmoid.

0 comments

nis25141310mo ago

Sigmoid (or the logistic function specifically rather) is exponential until you get close to the "turning point" (or rather, its growth bounded from below by an exponential). It's as you approach that point that it becomes linear, and after that its growth decays.

However you are sort of right that "churn" does not necessarily have to do with it being sigmoid because it will be anyway. It may be bring it earlier if the churn rate surpasses the user growth, but that's probably not important here.

thaumasiotesOP10mo ago

If the churn rate surpasses user growth, you won't go sigmoid, you'll stay exponential. You'll just be shrinking instead of growing. To be sigmoid, you need the growth rate to vary.

withinboredom10mo ago

Growth is not a function of users, though, it is a function of something else that *may* be exponential, for a time. Users don’t beget users (word-of-mouth doesn’t last forever; ad money has diminishing returns), and eventually your market will be saturated, so you can’t grow exponentially forever.

j / k navigate · click thread line to collapse