Question

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:

\((1\ -\ \frac{1}{3}=\frac{2}{3}=66\%)\)

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