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.
A very large quantity.
We have an exponential amount of explosives in my garage.