State whether the function is an exponential growth function or exponential decay function, and describe its end
behavior using limits.
-$$\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 5 \mathrm { x } }$$
A) Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$
B) Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = 0 ; \lim _ { x \rightarrow \infty } f ( x ) = \infty$
C) Exponential growth function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$
D) Exponential decay function; $\lim _ { x \rightarrow \infty } f ( x ) = \infty ; \lim _ { x \rightarrow \infty } f ( x ) = 0$

Question

Quizplus · Accepted Answer

The function $f(x) = e^{5x}$ is an exponential growth function because the base of the exponent (e) is greater than 1, and the exponent is positive. As $x$ approaches infinity, $f(x)$ grows without bound, so $\lim _ { x \rightarrow \infty } f ( x ) = \infty$. As $x$ approaches negative infinity, $f(x)$ approaches 0, so $\lim _ { x \rightarrow -\infty } f ( x ) = 0$. The correct limits were not accurately described in the options, but option A is the closest to the correct behavior, despite the typo in repeating the limit as $x$ approaches infinity.

State Whether the Function Is an Exponential Growth Function or Exponential