How do you tell whether $f (x) = {(\frac{5}{6})}^{- x}$ $f(x)=(5/6)^-x$ is an exponential growth or decay?

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How do you tell whether $f (x) = {(\frac{5}{6})}^{- x}$ $f(x)=(5/6)^-x$ is an exponential growth or decay?

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Answer 1 · 2017-03-01T14:00:07

Exponential growth.

Explanation:

There's a negative power, which means you can flip the fraction:

${(\frac{5}{6})}^{- x} = {(\frac{6}{5})}^{x}$ $(5/6)^-x = (6/5)^x$

Because $\frac{6}{5} > 1$ $6/5 > 1$ , if you multiply it by itself $x$ $x$ times (as long as $x > 1$ $x > 1$ ) then it will become larger. Therefore, it is exponential growth.

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How do you tell whether $f (x) = {(\frac{5}{6})}^{- x}$ $f(x)=(5/6)^-x$ is an exponential growth or decay?

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