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)}}}

Algebra ->  Trigonometry-basics -> 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)}}}      Log On


   

Question 1106283: which of the following represents exponential decay?
1.y=3%5E%280.45x%29
2.y=1.05%5E%280.35x%29
3.y=%281%2F3%29%5E%28-x%29
4.y=4%5E%28-1.25x%29
Answer by Edwin McCravy(20060) About Me  (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.y=3%5E%280.45x%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C3%5E%280.45x%29%29

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.y=1.05%5E%280.35x%29

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C1.05%5E%280.35x%29%29

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.y=%281%2F3%29%5E%28-x%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%281%2F3%29%5E%28-x%29%29

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

4.y=4%5E%28-1.25x%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%284%29%5E%28-1.25x%29%29

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:

y=a%5E%28bx%29%29, 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