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

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

Question
Exponential growth and decay
asked 2021-03-06

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

Answers (1)

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.
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