Question

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

Answer 1

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:

$y = 630(1.06)^{x}$

To solve for:

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

Solving:

Substitute 3 for x.

$y = 630(1.06)^{3}$

Include exponent:

$y = 630(1.191016)$

(Exact Amount)

Multiply:

$y = 750$

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.

$1.06 - 1 = 0.06$

There's a 6% growth.