Software metric for data growth
Apparently, the best you can do is write something on the lines of "the number of result sets is exponential in the number of input input elements". This is better than simply saying "the data grows exponentially" since such growth must happen with respect to some quantity. It also might be a good idea to state the value $2^n$ somewhere (in the more technical sections) so it is clear it is a precise and not an asymptotic estimate.

It is unfortunate you cannot estimate the size of each result set. Are you sure not even very conservative or even empirical estimates are possible? (If that is the case, then consider adding at least one of those.)