what is the percent rate of change in function y=(0.96)^x? Determine Whether The Function Represents Exponential Growth Or Exponential Decay?

A.) 4%, Decay
B.) 4%, Growth
C.) 0.4%, Growth
D.) 0.04%, Decay

Question

what is the percent rate of change in function y=(0.96)^x? Determine Whether The Function Represents Exponential Growth Or Exponential Decay?

A.) 4%, Decay
B.) 4%, Growth
C.) 0.4%, Growth
D.) 0.04%, Decay

zepdrix · Answer

So imagine a 1 in front, maybe that will help:$$\Large\rm y=1 \left(0.96\right)^x$$So for each integer value of x, how much is our 1 changing?
Let's try x=1.
What does our 1 change to?

zepdrix · Answer

I was tossing a lot of 1's around there -_-
Lemme just show you to clarify.
$$\Large\rm y=1(0.96)^1$$So multiplying this all out gives us:$$\Large\rm y=0.96$$

We started at 1, then we decreased to 0.96.
What percent did we decrease by?

anonymous · Answer

0.4%? Sorry It Took A While To Reply Had To Do Something. Thank You Though

anonymous · Answer

No Wait 0.04%

zepdrix · Answer

So the AMOUNT of decrease was 0.04.
And then ummm....

So the uh..
And we want this as a percent?
So we should move the decimal 2 places to the right maybe?

anonymous · Answer

Yes So It Would Be 4% Decay

zepdrix · Answer

Mmm yah that seems right :)

anonymous · Answer

Its Confusing Cause 0.04% Decays An Answer.

zepdrix · Answer

It might be easier to think about if you start with an amount like 100.
So at x=1, you're left with 96.

So you decreased by 4 ( out of 100 ).
4%

anonymous · Answer

Ahh Okay Well Thank You Again! :D