I don't know what you mean by "constant", since that usually refers to linear growth, which this clearly isn't.
As for the formula, take a closer look at it. For 64 squares, there was the first square, followed by 63 doublings. What is the power on the 2? 64? Or 63?
As for the domain and range, I'm not sure if they're referring to the whole-number domain (from 1 to 20) for the word problem, or the "all real numbers" domain for the function. They say "function", but you might want to ask your instructor, just to be sure...?