A random neuron fired in my brain and I was curious as to which grew faster, Fibonacci or n2. While I was at it I also plotted 2n.
Well as it turns out Fibonacci grows faster than n2 but that's nothing compared to how fast true exponential growth of 2n 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.