You are a Branch Manager and your office saw 2,500 patients in January 2012. From historical data, you know each month you add exactly 160 new patients and this trend will continue indefinitely. You also know each month your branch has an attrition rate (due to cancellation of services, patient death, etc.) of 5% of its total patient base and this trend will continue indefinitely.

Knowing the above and that the figures of 160 and 5% are fixed, please calculate the maximum number of patients your branch will ever see in a given month and explain how you arrived at that number.