How do you determine if $y = 0.2 {(5)}^{- x}$ $y=0.2(5)^-x$ is an exponential growth or decay?

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How do you determine if $y = 0.2 {(5)}^{- x}$ $y=0.2(5)^-x$ is an exponential growth or decay?

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Answer 1 · 2017-01-17T12:26:14

This is exponential decay. Two ways to tell are discussed below...

Explanation:

First, the negative exponent is an indicator of decay. You could rewrite the expression (without a negative exponent) as

$y = \frac{0.2}{5^{x}}$ $y=0.2/5^x$

This helps you to see that as $x$ $x$ gets very large, the expression gets very small - clearly not a case of growth.

Alternatively, you could make a chart in which you test increasing values of $x$ $x$ , starting at $x = 1$ $x=1$ (for example) and increasing slowly to $x = 5$ $x=5$ . You would see the results - the expression would decrease in value rapidly.

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How do you determine if $y = 0.2 {(5)}^{- x}$ $y=0.2(5)^-x$ is an exponential growth or decay?

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Explanation:

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How do you determine if $y = 0.2 {(5)}^{- x}$ $y=0.2(5)^-x$ is an exponential growth or decay?