If yes, of what type of function is it an example? Why might you identify it with that type of function? How do you identify a rational function? Can you give an example of a rational function?

Yes, the compound interest formula is a function of time and principle invested. As to the other questions, they seem to refer to a discussion your book or class are having about types of functions, and I am not sure just what is wanted here. Exceptions
are the last two questions, which refer to rational functions. Rational functions are functions that have fractions as part of the function. Another way to put this is to say that two polynomial expressions that form a fraction, as given in a function, make
that function a rational function.