Step 1

Determine weather for the following function is represent exponential growth or exponential decay. Then graph the function:

\(\displaystyle{f{{\left({x}\right)}}}={\left({0.8}\right)}^{{{x}}}\)

There is a general rule for the exponential function depending on the base of exponent as follows:

\(\displaystyle{y}={b}^{{{x}}}\ {b}\ {>}\ {1}\ \therefore\ \text{Represent for exponential growth function.}\)

\(\displaystyle{y}={b}^{{{x}}}\ {0}\ {<}\ {b}\ {<}\ {1}\ \therefore\ \text{Represent for exponential decay function.}\)</span>

For this function, \(\displaystyle\because\ {\left({0}\ {<}\ {b}\ {<}\ {1}\right)}\)</span>

\(\displaystyle\therefore\) This function is represent for exponential decay function.

Step 2

Determine weather for the following function is represent exponential growth or exponential decay. Then graph the function:

\(\displaystyle{f{{\left({x}\right)}}}={\left({0.8}\right)}^{{{x}}}\)

There is a general rule for the exponential function depending on the base of exponent as follows:

\(\displaystyle{y}={b}^{{{x}}}\ {b}\ {>}\ {1}\ \therefore\ \text{Represent for exponential growth function.}\)

\(\displaystyle{y}={b}^{{{x}}}\ {0}\ {<}\ {b}\ {<}\ {1}\ \therefore\ \text{Represent for exponential decay function.}\)</span>

For this function, \(\displaystyle\because\ {\left({0}\ {<}\ {b}\ {<}\ {1}\right)}\)</span>

\(\displaystyle\therefore\) This function is represent for exponential decay function.

Step 2