I want to quickly calculate how many steps S there are between some min and max, where n=min to start with, given some particular non-linear formula, e.g. n'=n * 1.01, n'' = n' * 1.01 etc. until n exceeds max.
The simplest way to determine S is to do so iteratively, i.e. step from min till we exceed max and count the total steps whose resultant values fell within the range.
However, does a fast analytical solution exist for this? Perhaps not only for this simple formula, but for any non-linear series? Or must we iterate to find the solution?