# Decide if the equation represents exponential growth or decay. Explain your answer. y=(3^x)^2

Question
Exponential growth and decay

Decide if the equation represents exponential growth or decay. Explain your answer. $$y=(3^{x})^{2}$$

2021-03-07
An equation of the form $$\displaystyle{y}={a}\cdot{b}^{{x}}$$ represent exponential growth when b>1 and represents exponential decay when b>1. $$\displaystyle{y}={\left({3}^{{x}}\right)}^{{2}}={\left({3}^{{2}}\right)}^{{x}}={9}^{{x}}$$
Since 9>1, $$\displaystyle{y}={\left({3}^{{x}}\right)}^{{2}}={9}^{{x}}$$ represent exponential growth.

### Relevant Questions

Determine whether each equation represents exponential growth or exponential decay. Find the rate of increase or decrease for each model. Graph each equation. $$y=5^x$$

Tell whether the function represents exponential growth or exponential decay. Then graph the function. $$f(x)=(1.5)^{x}$$

.

Tell whether the function represents exponential growth or exponential decay. Then graph the function. $$f(x)=(0.25)^{x}$$

Decide if the equation represents exponential growth or decay. Explain your answer. y=2^x/3^x
Decide if the equation represents exponential growth or decay. Explain your answer. $$\displaystyle{y}={\left(\frac{{{3}^{{x}}}}{{{2}^{{x}}}}\right)}$$
$$\displaystyle{g{{\left({t}\right)}}}={2}{\left({\frac{{{5}}}{{{4}}}}\right)}^{{t}}$$
Use exponential regression to find a function that models the data. $$\begin{array}{|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 \\ \hline \end{array}$$