You definitely want something exponential, so that you can express any quantity of time with a constant relative error. The precision of your estimation as well is very likely to be proportional to your estimation.
So you want something :
a) with integers
b) exponential
c) easy
Now why Fibonacci instead of, 1 2 4 8?
My guess is that it's because fibonacci grows slower. It's in goldratio^n, and goldratio=1.61...
