# Tell whether the function represents exponential growth or exponential decay. Then graph the function.f(x)=(0.25)^{x}

Tell whether the function represents exponential growth or exponential decay. Then graph the function. $f\left(x\right)=\left(0.25{\right)}^{x}$

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curwyrm

Step 1

Given: $f\left(x\right)=\left(0.25{\right)}^{x}$

Step 2

Thefunction represents exponential decay because it has the form $y=a{b}^{x}$. The decay factor is 0.25.

$\begin{array}{|ccccccc|}\hline x& -2& -1& 0& 1& 2& 3\\ y& 16& 4& 1& 0.25& 0.0625& 0.016\\ \hline\end{array}$

Step 3

In order to graph the function, we build a table of values:

$\begin{array}{|ccccccc|}\hline x& -2& -1& 0& 1& 2& 3\\ y& 16& 4& 1& 0.25& 0.0625& 0.016\\ \hline\end{array}$

Step 4

We plot the points from the table, then draw a smooth curve that begins on the right, just above the x-axis, passes through the plotted points and moves up to the left: