Exponential Inflation vs Hyperbolic Inflation

Chris Martenson has an interesting article entitled Our Money is Dying over at Peak Prosperity.  In it, he talks about the "inflationary spectrum", which consists of:

1. Non-inflationary price increases
2. Simple inflation
3. Loss of confidence in money
4. Hyperinflation, and finally
5. Currency destruction.  

See the article for a description of each.

Rather than seeing a single "inflationary spectrum", I instead see two quite distinct inflationary forces - one that is exponential, and one that is hyperbolic.  Let's briefly take a look at an exponential and hyperbolic functions (graphs):

The shapes, slopes, and positioning of the graphs come in many forms.  The key difference between exponential and hyperbolic, as explained by Wikipedia, is that:

• exponential growth grows to infinity as time goes to infinity (but is always finite for finite time),
• hyperbolic growth has a singularity in finite time (grows to infinity at a finite time).

Put another way, hyperbolic growth trajectories have a D-Day - a day of reckoning.

Now, relating this back to inflation, I have a crude (yet instructive) Inflation formula: