Hello Math Help Forum,

I'm working on a web script for a game that will increase a stat in diminishing returns depending on the value of that stat.

For instance, a user with 5000 Stat points will gain a 10% bonus to their stats per day, so it will be 5050 the next day.

However, I need to figure out a formula so users with higher Stat points, for example 10000, will receive less of a bonus. As an example I'll list how it should scale below (the checkpoints of 5000, 10000, 20000, etc were just doubled each time since I figured it would scale better if the checkpoints weren't as frequent as "every 5000 points". If it would be better to do it another way please tell me.)

5000 - 10% per day

10000 - 9% per day

20000 - 8% per day

40000 - 7% per day

80000 - 6% per day

160000 - 5% per day

And so on. This was my original idea, but then we would have a problem when it reaches below 1% because it would scale unevenly. I need a formula that will indefinitely scale down, so maybe something it should be reduced by 10% each time? For example,

5000 - 10% per day

10000 - 9% per day

20000 - 8.1% per day

40000 - 7.29% per day

80000 - 6.56% per day

160000 - 5.9% per day

(I rounded the percentages down for simplicities sake.)

So my question is, is there a formula that I could use so the returns will automatically diminish over time? Thanks for your time, and please tell me if I wasn't clear enough in my description.