1. Yes it is an exponential curve. 2. And it has a constant growth rate.
Here's the data set
It very obviously does not have a constant growth rate.
Yes it does. You would just take the average rate of growth of the money supply, plug that into the equation above and you would have a curve that closely approximates the curve above. Obviously the money supply growth probably varies from about 4-6% per year, but there is a best fit exponential curve that would map the data very well.