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Does the function model exponential growth or decay?

g(x)=(1)/(3)*((2)/(9))^(x)
Choose 1 answer:
(A) Growth
(B) Decay

Does the function model exponential growth or decay? $\newline$ $g(x)=\frac{1}{3} \cdot\left(\frac{2}{9}\right)^{x}$ $\newline$ Choose $1$ answer: $\newline$ (A) Growth $\newline$ (B) Decay

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Interpret the exponential function word problem

Full solution

Q. Does the function model exponential growth or decay?

\newline

g(x)=\frac{1}{3} \cdot\left(\frac{2}{9}\right)^{x}

\newline

Choose

1

answer:

\newline

(A) Growth

\newline

(B) Decay

Identify base: Step $1$ : Identify the base of the exponential function. In the function $g(x)=(\frac{1}{3})\cdot(\frac{2}{9})^x$ , the base of the exponential term is $(\frac{2}{9})$ .
Determine growth or decay: Step $2$ : Determine if the base is greater than $1$ or less than $1$ . If the base is greater than $1$ , the function models exponential growth. If the base is less than $1$ , the function models exponential decay.
Compare to $1$ : Step $3$ : Compare the base $(\frac{2}{9})$ to $1$ . Since $\frac{2}{9} < 1$ , the function represents exponential decay.
Choose based on analysis: Step $4$ : Choose the correct answer based on the analysis. Since the base $(\frac{2}{9})$ is less than $1$ , the function $g(x)=(\frac{1}{3})\cdot(\frac{2}{9})^x$ models exponential decay.

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