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
ANSWERED
asked 2021-05-28

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

Expert Answers (2)

2021-05-30
Answer is on video:
43
 
Best answer
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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