Are there any exponential-time iterative algorithms? Is it possible to implement an exponential-time algorithm using iteration, as opposed to recursion? I didn't have any particular algorithm in mind, I was just thinking theoretically.

The way I was thinking was to iterate not by adding 1, but by adding a small number j at the end of each loop. So the 3rd parameter in the for-loop would look like i+j instead of i++, and j would be really small (negative exponent perhaps? Like 2^-n)... Still, I'm not sure how such an algorithm could actually work, though.

Thanks for any input.
Yes. Given an input of length $n$, overwrite it and use the space to count to $2^n$ in binary.

Once you've done that, you could write out $2^n$ zeroes and then count to $2^{2^n}$ and so on, ad infinitum.