Calculating cost of servicing incremental number of users?

[MitchT]

Putting this is Science as there's no Maths forum. A science bod might be able to help...

Scenario:

I launch an app which costs 5p per month per user to operate.
On Day 1 it has no users.
At the end of Year 1 it has 1,200,000 users.

How much does it cost to run over Year 1, bearing in mind that the users increase gradually over the year?

Consideration:
It doesn't jump to 100k users at the end of Month 1, and 200k users at the end of Month 2, etc., so it's not a case of saying 5p x 100,000 to find out Month 1 costs as you don't have 100,000 users for all of Month 1... 200,000 users for all of Month 2... etc.

Thanks in advance!

[MitchT]

Thanks - makes perfect sense. Of course, it's more likely to start as a fairly flat curve and then get steeper as usage picks up. it's one of those things that'll either fall flat on its face or gain so many users so quickly that were crapping ourselves over the hosting bill!