Need math help.

Hello, /sci/.

I need some math wiz help. Can anyone tell me if the formula I need even exists?

f(a) = b

With each increase of "a", I need "b" to become larger, but be an increasingly smaller margin. For example, if a = 10, then b = 5, but if a = 20, then b = 7.

Can anyone help?

how about a logarithm function?  If you graph y = log(x), you see a growing curve that becomes less and less steep in slope as x increases.