I hope you'll permit me explicitly to single out your mocking invocation of my bête noire. I think that most non-technical authors just confuse 'exponential' with 'super-linear' (if they think even that quantitatively) … but I sometimes worry that even the somewhat more technically minded think that 'exponential' just means 'has an exponent', and so think that quadratic growth is exponential, y'know, because there's an exponent of 2.

time*n is linear in time and n, but ther symmetry stops there.

time^n is *geometric* (or polynomial) growth over time.

n^time is exponential in time.

time! (factorial) doesn't have a common name that I know. It is (in the long run) faster than any exponential growth.