Here are some examples where you enter the data directly into the bar:

exponential fit of {1,2,4,7,17}

http://www.wolframalpha.com/input/?i=exponential%20fit%20of%20%7B1%2C2%2C4%2C7%2C17%7D

exponential fit of {{0,1},{2,2},{4,4},{6,7},{8,17}}

http://www.wolframalpha.com/input/?i=exponential%20fit%20of%20%7B1%2C2%2C4%2C7%2C17%7D

There are no examples showing how this can be done with a dataset. I am not aware of any. It's very possible that the Wolfram|Alpha doesn't recognize that query yet for datasets. If a query doesn't work that you expect to, you can contact the Wolfram|Alpha team and leave them a suggestion at the bottom of the results page. This helps them know where to focus the future developement of Wolfram|Alpha.

Thank you. That helps, although I can't see what my options are for the words following the uploaded data. (My original question was about syntax and available commands/expressions/functions.) I'll look for "time series" and see what related options I might have.

I'm a high school teacher, and I don't want to spend too much time teaching a programming language to the students. I want to take the data and process it, with a little more power than Desmos, a little more availability than the commands on a TI graphing calculator. I hope that makes sense.

Yes. Sorry for the ambiguity. I mean the search field (with the equal-sign submit button) at wolframalpha.com.

Thank you. Your suggestion is probably good, but I'm looking for commands I can enter into the Wolfram command line, or some other way to run "exponential fit" against my uploaded data.