Step 1

We are given the function:

\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{3}}}}\right)}^{{{x}}}\)

Step 2

We identify the value of the base. The base, \(\displaystyle{\frac{{{1}}}{{{3}}}},\) is greater than 0 and smaller than 1, the function represents exponential decay.

Step 3

We make a table of values:

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{y}\backslash{h}{l}\in{e}-{2}&{9}\backslash{h}{l}\in{e}-{1}&{3}\backslash{h}{l}\in{e}{0}&{1}\backslash{h}{l}\in{e}{1}&{\frac{{{1}}}{{{3}}}}\backslash{h}{l}\in{e}{2}&{\frac{{{1}}}{{{9}}}}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

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:

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

We are given the function:

\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{3}}}}\right)}^{{{x}}}\)

Step 2

We identify the value of the base. The base, \(\displaystyle{\frac{{{1}}}{{{3}}}},\) is greater than 0 and smaller than 1, the function represents exponential decay.

Step 3

We make a table of values:

\(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{y}\backslash{h}{l}\in{e}-{2}&{9}\backslash{h}{l}\in{e}-{1}&{3}\backslash{h}{l}\in{e}{0}&{1}\backslash{h}{l}\in{e}{1}&{\frac{{{1}}}{{{3}}}}\backslash{h}{l}\in{e}{2}&{\frac{{{1}}}{{{9}}}}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

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:

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