contestada

What is the percent rate of change in function y = \((0.99)^x\)? Determine whether the function represents exponential growth or exponential decay.

1%; exponential growth
1%; exponential decay
10%; exponential growth
0.1%; exponential decay

Respuesta :

scme1702
1%; exponential decay
This is because the value remaining is 99% of the original value and the change is exponential.

Answer: The correct answer is 1%: exponential decay.

Explanation: We are given a function:

[tex]y=(0.99)^x[/tex]   ...(1)

To determine the percentage rate of change in function, we compare the given function with the general form of exponent function, which is:

[tex]y=a(1+r)^x[/tex]    ...(2)

Comparing both the equations, we get:

[tex]1+r=0.99[/tex]

[tex]r=-0.01[/tex]

We take 'r' in percentage, so converting this above value in percentage, we get:

[tex]r=-0.01\times 100=-1\%[/tex]

As the value of 'r' is negative, it means that the exponent is decaying, so the percentage rate of change in function will be 1% and it will be exponential decay.