How do you determine if the equation #y=(1/2)^x# represents exponential growth or decay?
1 Answer
Jul 12, 2016
The function decays exponentially.
Explanation:
Intuitively, you can determine if a function is exponentially growing (heading toward infinity) or decaying (heading toward zero) by graphing it or simply evaluating it at a few increasing points.
Using your function as an example:
It is clear that as
graph{(1/2)^x [-2.625, 7.375, -0.64, 4.36]}
You can see that the function rapidly approaches zero as
The rule to work by is that for