Question

# Tell whether the function represents exponential growth or exponential decay. Identify the percent increase or decrease. Then graph the function. f(x)

Exponential growth and decay

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

2021-05-30
2021-08-04

Step 1
We are given the function:
$$(f(x)=\left(\frac{1}{3}\right)^{x}\$$

Step 2
We identify the value of the base. The base, $$(\frac{1}{3},)$$ is greater than 0 and smaller than 1, the function represents exponential decay.
Step 3
We make a table of values:
$$\begin{array}{|c|c|}\hline x & y \\ \hline -2 & 9 \\ \hline -1 & 3 \\ \hline 0 & 1 \\ \hline 1 & \frac{1}{3} \\ \hline 2 & \frac{1}{9} \\ \hline \end{array}$$
Step 4
We plot the points from the table. Then draw a smoth curve from right to left, that begins just above the x-axis, passes throigh the plotted points and moves up to the left.

Step 5
The percent of decrease is:
$$(1\ -\ \frac{1}{3}=\frac{2}{3}=66\%)$$