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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

Verified Answer :

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:

\(y=(0.99)^x\)   ...(1)

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

\(y=a(1+r)^x\)    ...(2)

Comparing both the equations, we get:

\(1+r=0.99\)

\(r=-0.01\)

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

\(r=-0.01\times 100=-1\%\)

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.