I'm looking for a function that:
- is monotonically decreasing over the range {$x = 1, x = 50$} where $x$ can only take integer values
- Decreases gently at first, then steeply as $x$ gets closer to $50$.
What's a simple function that meets these criteria? All the examples I've managed to find so far are very complicated. I could for example use Lagrange interpolation to interpolate over all 50 points, but the resulting expression is massive. I could use fewer points, but then the function ceases to be monotonically decreasing.
It'd be nice if the function has some way to control how gentle is "gentle" or where the function starts decreasing quickly, but at this stage of my use case, the exact specifics of the function are not important as long as it meets the two criteria above.
