I just wrote a blog post and wasn't sure how to word a particular sentence. Say I have the following function:
\begin{equation} f(x) = x^2 \end{equation}
Then I can say that the value of f(x) grows quadratically with x*. Similarly with this function:
\begin{equation} f(x) = e^x \end{equation}
...I could say that f(x) grows exponentially with x. But what about this?
\begin{equation} f(x) = x! \end{equation}
Do I say that f(x) grows "factorially"? What's the proper term?
*I worded this wrong at first. It should be right now. Wait, is that even right? Or would "exponentially" imply f(x) = kx? Should the first term be "quadratically" instead?