Modeling a curve - Time Series or Fitting a Distribution?

Question

I have a curve that looks like this:

This is an ARPDAU curve (Average Revenue Per Daily Active User). I have data about how Users interact with a product where the curve is created by:

$$\dfrac{\text{Total Revenue Day N}}{\text{Total Users On Day N}}.$$

What I would like to do it model this curve and make predictions further out. The curve here is from 0 - 365. It's not always the case when I have full data. A more common scenario would have 30-60 days of data and project out to 365.

My questions are:

1. What is the best way to model this curve? I know there are time series methods or fitting the curve to some type of distribution.

2. Which packages are the most preferable in either R or Python?

Any help or comments would be greatly appreciated! Thank you in advance.