Which function grows at the fastest rate for increasing values of x? p(x)=1/2x^3+9 g(x)=14x f(x)=2x^2−x h(x)=3^x

Out of all of these choices    the answer is h(x) = 3ˣ as exponential functions grow faster than polynomial functions for large values of x.functions p, g, and f are all polynomial functions.why? well, for an intuitive outlook, notice how the polynomial functions have a fixed exponent. but for function h, the exponent is the variable. h will grow faster.for polynomial functions, the exponent is constant but the base changes.3² = 9, 4² = 16, 5² = 25, 6² = 36for exponential functions, the base is constant but the exponent changes3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729you can see that it grows so much faster for larger x. it's tripling for each increase of 1 in x.

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