How do you determine if the equation #f(x) = 5(1/6)^x# represents exponential growth or decay?

1 Answer
Feb 17, 2016

Logic corrected!#" "-> " decay"#

Explanation:

Tony B

Total rewrite!

Consider the case of: #" "x<0#

We have: #5/((1/6)^x) = (5xx6^x)/(1^x) = 5xx6^x#

Thus as the magnitude of negative #x# increases the value of y also increases.

So as {x: x < 0} increases (moved to the right) it is the reverse of what I previously wrote, so we have decay.

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Consider the case of #" "x=0#

We have: #" " 5(1/6)^0 = 5xx1 = 5#

also we have:

#5(1/6)^(-0)>5(1/6)^0>5(1/6)^(+0)#

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Consider the case of #" " 0 < x#

The denominator of #1/6# increases as #x# increases in #(1/6)^x#
So #(1/6)^x# becomes smaller and smaller as #x# increases.

This means that #5(1/6)^2# decreases as #x# increases.

So again we have decay

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In conclusion: the equation is in decay