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

Respuesta :

Answer:

4% decay

Therefore, option A is correct.

Step-by-step explanation:

We have been given a function:

[tex]y=(0.96)^x[/tex]

Our general equation of exponential decay is:

[tex]y=a(1-\frac{b}{100})^x[/tex]

On comparing the decay with general equation we get:

[tex]1-\frac{b}{100}=0.96[/tex]

On simplification:

[tex]\frac{b}{100}=.96-1[/tex]

[tex]\frac{b}{100}=-0.04[/tex]

[tex]b=4%[/tex]

Hence, 4% decay

Therefore, option A is correct.