Question

A town has a population of 17,900 and shrinks at a rate of 9% every year. Which equation represents the town’s population after 5 years?
Answer
Multiple Choice Answers
P, equals, 17, comma, 900, left parenthesis, 1, minus, 0, point, 0, 9, right parenthesis, to the power 5P=17,900(1−0.09)
^5

P, equals, 17, comma, 900, left parenthesis, 1, minus, 0, point, 0, 9, right parenthesisP=17,900(1−0.09)
P, equals, 17, comma, 900, left parenthesis, 0, point, 0, 9, right parenthesis, to the power 5P=17,900(0.09)
^5

P, equals, 17, comma, 900, left parenthesis, 1, minus, 0, point, 9, right parenthesis, to the power 5P=17,900(1−0.9)
^5

Answer 1

To calculate the population of the town after 5 years with a 9% annual decrease, we start with the population formula for exponential decay:

\[
P = P_0(1 - r)^t
\]

where:
- \(P_0\) is the initial population (17,900),
- \(r\) is the rate of decrease (9%, or 0.09),
- \(t\) is the time in years (5).

Substituting in the values:

\[
P = 17,900(1 - 0.09)^5
\]
\[
P = 17,900(0.91)^5
\]

So, the correct equation that represents the town’s population after 5 years is:

\[
P = 17,900(1 - 0.09)^5
\]

This corresponds to the first option in your multiple choice answers:

**P = 17,900(1 - 0.09)^5**