O(N^2) is not exponential but just polynomial. O(2^N) is still exponential. O(N!) and O(N^N) are faster than exponential but not that much; O(N^N) grows slower than O(N!)[1].

Hyper-exponential is most likely double exponential O(a^b^N). There is an exponential growth of apps on these platforms and another exponential growth of users on these apps.

[1] http://en.wikipedia.org/wiki/Stirling's_approximation