## Figuring out replacements

Greetings,

Here's my current problem that I'm having a hard time wrapping my head around:

Cumulative filtration capacity is growing at 12% per year. Five years after new construction, filters need to be replaced, as well as every five years thereafter. Given the cumulative capacity, determine the number of new and replacement filters required.

2010: 57,000
2011: 63,850
2012: 71,500
2013: 80,000
2014: 89,700
2015: 100,500

So the filters required for new construction is easy - (capacity year n) - (capacity year n-1), or 6,850 in 2011 and so on. It's the replacement I'm having a hard time with given the growth rate. I can break it down into (capacity year n - replacement period) - (capacity year n - replacement period - 1) (in other words, the new construction 5 years ago), but then I also have to do that for 5 years ago, 10 years ago, etc. Is there a way to get a "replacement factor" or something based on the installed capacity from a year ago? I expect it's somewhat less than 20%, but am not sure how to figure it out.