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Recall that the general form of an exponential function is $y=ab^x,$ where $a \neq 0$ is a factor that can shrink, stretch, or reflect the function. The base $b$ must be positive. If $a>0$ and $b>1,$ then we have an exponential growth function and $b$ is called the growth factor.
On the other hand, if the base is $a>0$ but $0 we have an exponential decay function and $b$ is known as the decay factor.
We can compare the given function $y=\frac{1}{3}e^x$ to the general form of an exponential function to identify its parameters and determine if it represents exponential growth or exponential decay. $\begin{gathered} y={\color{#0000FF}{a}}{\color{#009600}{b}}^x \qquad y={\color{#0000FF}{\frac{1}{3}}}{\color{#009600}{e}}^x\\[0.5em] \Downarrow\\[0.5em] {\color{#0000FF}{a}}={\color{#0000FF}{\frac{1}{3}}} \qquad {\color{#009600}{b}}={\color{#009600}{e}} \end{gathered}$ Notice that $a = \frac{1}{3}$ is positive. Furthermore, the base is the natural base $e$, which has an approximate value $e \approx 2.718281\ldots$ and is greater than $1.$ Hence, the function $y=\frac{1}{3}e^x$ represents exponential growth.