# Simple formula for exponential growth

Is there a simple formula that describes exponential growth? What are the key factors driving such behavior? Well, it turns out there is… but BEWARE! Let this formula’s simplicity do not fool you. It may look simple, but REALLY HARD to achieve.

Now that you are prepared, let’s take a look at it:

Let’s recall the simple system I’ve covered before:

This system incorporates 2 feedback loops:

1. Reinforcing loop — the more active users we have the more new users are coming by means of viral, ASO & paid loop covered in previous post. The more users are coming the more active users we have — this is why it is reinforcing. Effectively, New Users = Active Users * k
2. Balancing loop — the more active users we have the more users we lose because of churn. The more users we lose the less is active users — this is why it is balancing. Similarly, Churned Users = Active Users * (1 — retention), since churn rate is reverse of retention.

There are 3 possible scenarios for this equation:

1. k > (1 — retention)
2. k = (1 — retention)
3. k < (1- retention)

The graph of active users below illustrates all 3 cases (for simplicity I use churn instead of (1- retention) on this graph since these are equivalent):

I think this formula has 3 key consequences:

1. It balances app developer’s attention between retention and viral & other growth loops. Gives more levers to try.
2. Sometimes developers are so obsessed about k-factor being over 1, that they easily forget about retention. Of course, you can make all users to attract more than 1 new user with some “dirty tricks” (i.e. growth hacks) like auto-inviting Facebook friends or spamming contacts from address book, but those users will just uninstall the app & never come back.
3. (1 — retention) almost always is less than 1, so it is easier to achieve than just k > 1 ☺

That is why I think this formula is much more accurate & driving action than the famous k > 1.

Have fun & good luck in achieving exponential growth!