Final answer:
The correct answer is C. f(x)=e^{-3x}, which is an exponential decay function because it has a constant base e and a negative exponent that indicates decay.
Step-by-step explanation:
The correct option for an exponential decay function from the choices provided is C. f(x)=e^{-3x}. The reason this represents exponential decay is because the base of the exponent is the irrational number e (approximately 2.71828), which is a constant used often in mathematics for continuous growth or decay, and the exponent is negative, indicating decay. In this function, as x increases, f(x) decreases towards zero.
For clarification, functions A and D are not decay functions because the exponents are not constant negative values, and function B is not a function of x.