How is an exponential function different from a polynomial function? Examples?

Answer 1

polynomials may have "wiggles" in them, and have either
(a) a max or a min
(b) go from -∞ to +∞

pure exponentials (y=a*b^x) have a horizontal asymptote at y=0
are always positive or negative, depending on the sign of a
at some point they grow faster than any polynomial, no matter how high a degree