Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y=3800(0.97)
x

Answer 1

All exponential functions can be viewed as a rate of change based off of 100%.

In a standard exponential function, your general form is
`f(x) = a\cdot b^x` and it's the b-value that indicates if it's growth or decay.

If b > 1, then this means you'll end up with more than 100% of what you started with, so you'll have growth.

If b < 1 (but also b > 0 for all exponential functions), then it means you have less than 100%, so you'll have decay.

Now to find the percent growth or decay, you have to look at that b-value and figure out how far from 100% is it.

In this functions, b = 0.97 or 97%. So how much less than 100% is that? It's 3% less, so this is a decay situation, where it decays by 3% for each x-value increase by 1-unit.

If b > 1, then b - 1 = growth rate.

If b < 1, then 1 - b = decay rate.

It's all about how far from 100% you will be.

Answer 2

Answer: 3% decay, decay function

Explanation:

.97 is the rate and it is less than 1 so the function is a decay

1 - .97 = .03 => 3% decay