Question

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

y=57(0.4)^x

Answer 1

Decay, 60%

Explanation:

Remember that the exponential function is written in the form
`y=ab^x`. In this problem, a=57 and b=0.4. A function is considered a growth function when
`b>1`. Since 0.4 not greater than 1, this is an exponential decay function.

Now, to find the rate of decrease we can use part of the form
`y=a(1-r)^x`.

`1-r` represents the percentage decrease, in this case, 0.4. If that entire term is 0.4, we need to solve for
`r`.

`1-r=0.4\\r=0.6`

So, the rate of percentage decrease is 60%.

I hope this helps!