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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

Verified Answer :

Answer:

4% decay

Therefore, option A is correct.

Step-by-step explanation:

We have been given a function:

\(y=(0.96)^x\)

Our general equation of exponential decay is:

\(y=a(1-\frac{b}{100})^x\)

On comparing the decay with general equation we get:

\(1-\frac{b}{100}=0.96\)

On simplification:

\(\frac{b}{100}=.96-1\)

\(\frac{b}{100}=-0.04\)

\(b=4%\)

Hence, 4% decay

Therefore, option A is correct.

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