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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=630(1.06)^x y=630(1.06) x

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MathWiz0001

Step-by-step explanation:

To identify a growth or decay, we need to figure out the parts of the equation.

Let's include a real-world situations as an example.

Amelia's car payment is $630 every month, and the cost increases by 6%. Let x represent the amount of months.

Given:

[tex]y = 630(1.06)^{x} [/tex]

To solve for:

  • Whether it's a growth or decay.
  • Determine the percentage rate.

Solving:

Substitute 3 for x.

[tex]y = 630(1.06)^{3} [/tex]

Include exponent:

[tex]y = 630(1.191016)[/tex]

(Exact Amount)

Multiply:

[tex]y = 750[/tex]

Approximately.

The equation is a growth since the value has increased.

Percentage rate?

The value in our parentheses determines our growth or decay.

  • Having a value less than one creates a decay.
  • Having a value greater that one creates a growth.
  • 1 on a graph is a straight line, neither.

We can easily determine it's a growth, but by how much?

Subtract 1 from 1.06.

[tex]1.06 - 1 = 0.06[/tex]

There's a 6% growth.

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