Model churn when churn rate diminishes over time If I'm calculating a consistent rate, it's easy to model that as exponential decay. For example, if I lose 10% of customers each year, starting with A customers. $$ y = A 0.9^x $$ However, what if that churn is less with each year. Rather than $ A * 0.9 * 0.9 * 0.9 ... $ I need $ A * 0.9 * 0.88 * 0.86 ... $ or something along those lines. Is there a standard way to model something like that?

You can create a function like that, e.g., $$y=A*(0.9-0.02x)^x \ ,$$ for $x=1,2,\ldots$. But it leaves 2 questions:

* Does this equation makes sense in terms of your model? Is there data available that fits in this model? And, in this specific case, what should we do for $x>45$?

* Is the expression in the equation both accurate in therms of modelling but still easy enough so that you can obtain some other properties of the model that you may be interested in?