Question

Determine whether the function represents exponential growth or exponential decay. Then graph the function.
\(\displaystyle{y}={\left({0.8}\right)}^{{{x}}}\)

Answer 1

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