How do you determine if the equation #f(x) = 2(1/2)^x# represents exponential growth or decay?

1 Answer
Sep 16, 2016

#f(x)# is decay

Explanation:

#color(brown)("Moving to the right on the number line")#

As #x# becomes ever greater then #(1/2)^x# becomes less and less but still positive.

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#color(brown)("Moving left on the number line")#

When #x<0# we have #2(2/1)^(|x|)#

The more and more negative #x# becomes the greater #2(2/1)^(|x|)#
becomes. However in doing so we are moving further from 0 in the negative direction. Consequently changing this direction so that you move closer to 0 then #2(2/1)^(|x|)# is decreasing
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Thus #2(1/2)^x# is always decreasing as you move to the right.

#lim_(x->oo) 2(1/2)^x ->0#

Tony B