A random neuron fired in my brain and I was curious as to which grew faster, Fibonacci or n^2. While I was at it I also plotted 2^n.
Well as it turns out Fibonacci grows faster than n^2 but that's nothing compared to how fast true exponential growth of 2^n grows.
Here's some pretty pictures.
Notice that the y-axis is logarithmic, exponential growth is fast!
If you have trouble imagining what that really looks like, here is with a linear axis.