Question

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

Answer 1

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.

Answer 2

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