SOLUTION: which of the following represents exponential decay? 1.{{{y=3^(0.45x)}}} 2.{{{y=1.05^(0.35x)}}} 3.{{{y=(1/3)^(-x)}}} 4.{{{y=4^(-1.25x)}}}

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Question 1106283: which of the following represents exponential decay?
1.
2.
3.
4.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Exponential decay is always represented by a curve that's
going down on the far right, approaching a horizontal line,
usually the x-axis. 

1.



No, that's going up on the right, so it's not going down 
approaching a horizontal line on the far right, so it's not 
decaying.

2.



No, that's going up on the right very slowly, so it's not 
going down approaching a horizontal line, so it's not 
decaying.

3.



No, that's going up on the right, so it's not going down 
approaching a horizontal line, so it's not decaying.

4.



Yup, that's going down approaching the x-axis,
so it's the only one decaying.

The rule is this. If its equation is of the form:

, where a is positive and not 1, and
b is not 0.

then 

if a > 1, then b < 0 (b must be negative) in order to have 
exponential decay (approaching the x-axis on the right from 
above).

if a < 1, then b > 0 (b must be positive) in order to have 
exponential decay (approaching the x-axis on the right from 
above).

Edwin

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