Say I have a number of items, how can I express mathematically that I only want to use a certain amount of them, that goes down as the number grows?
For example, for small numbers like 3, I want to use everything the full set (100%). As we approach 7-8, then I would like to use 5 (62-71%) and as we get up to 40-50, then use 7-8 of them (17-20%) etc. Eventually getting up to 100+ items, then we should max use 10-15 of them (10-15%).
Note for large sets the number shouldn't approach zero. I considered the function:
$$\frac{x}{x^{2}}$$
but obviously this isn't approriate. My attempts to include fractions in the denominator perform well for large numbers, but results percentages over 100 for small numbers. Perhaps I could always round it down to 1, but is there a better approach?
Edit: Wasn't sure what the most appropriate tags for the question were.
Exponential decay functions solve the problem well if I set a limit on the maximum decay:
$$i * 0.96^{\frac{1}{2}i_{p}}$$
where $i_{p} = i$ but $i_{p}$ stops at a max of 150.