I'm trying to answer a preparation question in math, but I don't get it, so an formula with an explanation would be very helpful!
In a simple system measuring recent user activity each user have one personal counter. This counter increases by one each time the user is active, but only if the current minute is not equal to the previous minute(so, max +1 per minute). At midnight the counter is decreased by 15%.
So, if a user is increasing the activity counter by 100 each day the value after the first midnight will be 85 (100 - 15%). After the second midnight the counter value will be 157.25 (185 - 15%).
Questions
How many days will it take to reach a value of 650 when increasing the counter by 100 before it decreases with 15% and the counter is currently at 350(before the 100 increase)?
If the systems rounds the number after removing the 15%, how many days will it take to reach the maximum value when starting at zero and increasing the counter by 100 before it decreases and gets rounded? What is the maximum value?
I think the answer to 1. is 17 days, and the answers to 2. is the end of day 33, with a value of 664. I solved this by simply repeating the steps, but I need to know the formulas.
Can anyone help me with this? :)