Tell whether the function represents exponential growth or exponential decay. Then graph the function f(x)=\frac{1}{3}e^{x}

Burhan Hopper 2021-07-28 Answered
Tell whether the function represents exponential growth or exponential decay. Then graph the function.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{3}}}}{e}^{{{x}}}\)

Want to know more about Exponential growth and decay?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Theodore Schwartz
Answered 2021-07-29 Author has 25878 answers

Step 1
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{3}}}}{e}^{{{x}}}\)
Step 2
We identify the value of the base. The base, e, is greater than 1, thus the function represents exponential growth.
Step 3
\(\begin{array}{|c|c|}\hline x & y \\ \hline -2 & 0.045 \\ \hline -1 & 0.123\\ \hline 0 & 0.333\\ \hline 1 & 0.906\\ \hline 2 & 2.463\\ \hline 3 & 6.695\\ \hline \end{array}\)
Step 4
We plot the points from the table. Then we draw a smoth curve from left to right, that begins just above the x-axis, passes through the plotted points and moves up to the right.
image

Not exactly what you’re looking for?
Ask My Question
13
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...