Scope of term? 

Is the term hyperbolic growth used for:
 all growth towards a mathematical singularity (i.e., any function that goes to infinity in finite time), or
 only growth that looks like a hyperbola?
I ask because, for instance,  has a singularity (at 0), but the graph is not a hyperbola: thus, strictly speaking, it is not hyperbolic, but perhaps the term is used loosely by analogy.

Any references or experts? Thanks!

Nils von Barth ()