Re: Exponential growth ... a^t, for a an integer
any real number greater than 1
Why stop there? For reals in (0,1), you have exponential growth in the value's smallness. For 0 and 1, you have exponential growth in the value's sameness. "This 1 is much more the same than it was yesterday!"
Daft explanations of exponential "growth" for negative reals and complex numbers with non-zero imaginary parts are left as an exercise for the reader. Many of whom, I'm sure, could use the exercise.
 Silly as that is, it reminds me a bit of Matt Skala's famous essay "What Colour are your bits?", where he considered how people may assign different interpretations to identical values based on their provenance.
 Pretty easy for integer exponents.