How do you determine if the equation $y = 2 {(\frac{1}{4})}^{x}$ $y = 2(1/4)^x$ represents exponential growth or decay?

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Answer 1 · 2017-10-07T06:27:14

Growth/decay equations are always in the form:

$y = a {(b)}^{x}$ $y=a(b)^x$ where $a =$ $a=$ initial amount, $b =$ $b=$ growth/decay factor,

and $x =$ $x=$ time

If $b > 1$ $b>1$ , then the amount will get larger so exponential growth

If $b < 1$ $b<1$ , then the amount will get smaller so exponential decay

if $b = 1$ $b=1$ , then the amount will stay the same so its neither growth or decay. It’s just a constant value.

In your case, $b = \frac{1}{4}$ $b=1/4$ and $\frac{1}{4} < 1$ $1/4<1$ so it is exponential decay.

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