Question

Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y = 26(0.904)

Answer 1

Answer: Decay rate of 9.6%

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Step-by-step explanation:

I'm assuming you meant to write y = 26(0.904)^x

This is in the form y = a*b^x with a = 26 as the initial value and b = 0.904 represents the term tied to the growth rate.

Set b equal to 1+r to find that

1+r = b

1+r = 0.904

r = 0.904-1

r = -0.096

The negative r value indicates we have exponential decay. Specifically we have a decay rate of 9.6%

This means the amount of items are decreasing by 9.6% each time.

For example, if we started with 1000 people, then the population goes down by 0.096*1000 = 96 to end up with 1000-96 = 904 people by the end of year 1. We could also compute 1000*0.904 = 904. In this example, I'm using a = 1000 and b = 0.904