Question

Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y = 3900(1.86)

Answer 1

• growth
• 86% per time unit

Explanation:

You want to know if the function y = 3900(1.86^x) represents growth or decay, and at what rate.

Exponential function

An exponential function can be written in the form ...

y = (initial value)(growth factor)^x

where ...

growth factor = 1 + growth rate

Growth rate

Solving for the growth rate, we find ...

growth rate = growth factor - 1

Comparing the given equation to the above form, we see ...

initial value = 3900

growth factor = 1.86

Then the growth rate is ...

growth rate = 1.86 - 1 = 0.86 = 86%

When the growth rate is positive, the function represents growth, not decay.

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