How do you determine if the equation #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# where #a=#initial amount, #b=#growth/decay factor,

and #x=#time

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

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

if #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=1/4# and #1/4<1# so it is exponential decay.