Question 1106283
<pre>
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^(0.45x)}}}

{{{graph(400,400,-5,5,-5,5,3^(0.45x))}}}

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^(0.35x)}}}

{{{graph(400,400,-10,10,-10,10,1.05^(0.35x))}}}

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=(1/3)^(-x)}}}

{{{graph(400,400,-5,5,-5,5,(1/3)^(-x))}}}

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^(-1.25x)}}}

{{{graph(400,400,-5,5,-5,5,(4)^(-1.25x))}}}

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^(bx))}}}, 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</pre>