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1.
Applies to any rate of growth which is larger than some expected rate of growth.

In common usage, however, only a small sample size is available, and exponential applies to sufficiently large positive rate of growth.

In mathematical terms, exponential growth is "superlinear"
Person 1: The number of African American presidents in the US is growing exponentially.

Person 2: That's right!

Person 1: The ant population in my kitchen seems to double every week.

Person 2: Oh... well at least it's not growing exponentially

Person 3: x log x grows exponentially.
by FineHall October 14, 2009
 
2.
A very large quantity.
We have an exponential amount of explosives in my garage.
by Gary Coleman IV June 17, 2008