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Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y = 9200(1.018)²

Given the following exponential function, identify whether the change represents growth-example-1
User Zvyn
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1 Answer

19 votes
19 votes

Answer:

growth

1.8%

Explanation:

If the number raised to the power x is between 0 and 1, it is decay since as the exponent increases, the value of the power expression decreases.

For example, think of 0.1, a number between 0 and 1.

0.1^x

x = 1, 0.1^1 = 0.1

x = 2, 0.1^2 = 0.01

x = 3, 0.1^3 = 0.001

As you see, as x increases, the value of the expression decreases from 0.1 to 0.01 to 0.001

Now look at a power in which the base is greater than 1.

If the number raised to the power x is greater than 1, it is growth since as the exponent increases, the value of the power expression increases.

For example, look at 1.5^x

1.5^x

x = 1, 1.5^1 = 1.5

x = 2, 1.5^2 = 2.25

x = 3, 1.5^3 = 3.375

As you see, as x increases, the value of the expression increases from 1.5 to 2.25 to 3.375.

Now our problem:

y = 9200(1.018)^x

What base is raised to x?

Answer: 1.018

Since 1.018 is greater than 1, as the exponent, x, increases, the value of 1.018^x increases. Therefore, this is exponential growth.

1.018 = 1 + 0.018 = 1 + 1.8%

The percentage is 1.8%

User James Conkling
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