State whether the function is an exponential growth function or exponential decay function, and describe its end
behavior using limits.
-$$f ( x ) = 3 ^ { - x }$$
A) Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$
B) Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$
C) Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$
D) Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$

Question

Quizplus · Accepted Answer

The function $f(x) = 3^{-x}$ is an exponential decay function because the base (3) is raised to a negative exponent (-x). As $x$ approaches infinity, $f(x)$ approaches 0, indicating decay.

State Whether the Function Is an Exponential Growth Function or Exponential