It will be handy to have some simple criteria to tell when a function is growing more or less exponentially.
Proposition.
Let 
be measurable,
and suppose that for some sequence
we have
Let
and
IF a>0 and 
then f grows more or less exponentially,
with rate a and factor K.
qed
Corollary. In particular, if
and
then f grows more or less exponentially,
with rate 
and factor R.
qed