A town has a population of 141,200 and shrinks at a rate of [tex]$6 \%$[/tex] every year. Which equation represents the town's population after 8 years?

A. [tex]P = 141,200(1-0.06)(1-0.06)(1-0.06)(1-0.06)[/tex]

B. [tex]P = 141,200(1-0.06)^8[/tex]

C. [tex]P = 141,200(1.06)^8[/tex]

D. [tex]P = 141,200(1-0.6)^8[/tex]

To find the town's population after 8 years, we can use the exponential decay formula. Here's how you can solve the problem step-by-step:

1. Identify the Initial Population: The initial population of the town is 141,200.

2. Recognize the Shrinking Rate: The town's population shrinks by 6% each year. This means the population remains 94% of its size each year because 100% - 6% = 94%, or in decimal form, 0.94.

3. Determine the Number of Years: We want to know the population after 8 years.

4. Write the Exponential Decay Formula: To find the population after a certain number of years with a constant shrinkage, use the following equation:

[tex]\[
P = \text{{initial population}} \times (1 - \text{{shrink rate}})^{\text{{number of years}}}
\][/tex]

In this case, it translates to:

[tex]\[
P = 141,200 \times (1 - 0.06)^8
\][/tex]

5. Calculate the Result: Now, compute:

[tex]\[
P = 141,200 \times 0.94^8
\][/tex]

By evaluating this expression, the population after 8 years is approximately 86,071.

Therefore, the equation that represents the town's population after 8 years is:

[tex]\[
P = 141,200(1 - 0.06)^8
\][/tex]