# Tell whether the function represents exponential growth or exponential decay. Then graph the function f(x)=\frac{1}{3}e^{x}

Tell whether the function represents exponential growth or exponential decay. Then graph the function.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{3}}}}{e}^{{{x}}}$$

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Theodore Schwartz

Step 1
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{3}}}}{e}^{{{x}}}$$
Step 2
We identify the value of the base. The base, e, is greater than 1, thus the function represents exponential growth.
Step 3
$$\begin{array}{|c|c|}\hline x & y \\ \hline -2 & 0.045 \\ \hline -1 & 0.123\\ \hline 0 & 0.333\\ \hline 1 & 0.906\\ \hline 2 & 2.463\\ \hline 3 & 6.695\\ \hline \end{array}$$
Step 4
We plot the points from the table. Then we draw a smoth curve from left to right, that begins just above the x-axis, passes through the plotted points and moves up to the right.