A town has a population of 141,200 and shrinks at a rate of 6% every year. Which equation represents the town’s population after 8 years? Answer Multiple Choice Answers P, equals, 141, comma, 200, left parenthesis, 1, minus, 0, point, 0, 6, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 6, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 6, right parenthesis, left parenthesis, 1, minus, 0, point, 0, 6, right parenthesisP=141,200(1−0.06)(1−0.06)(1−0.06)(1−0.06) P, equals, 141, comma, 200, left parenthesis, 1, minus, 0, point, 0, 6, right parenthesis, to the power 8P=141,200(1−0.06) 8 P, equals, 141, comma, 200, left parenthesis, 1, point, 0, 6, right parenthesis, to the power 8P=141,200(1.06) 8 P, equals, 141, comma, 200, left parenthesis, 1, minus, 0, point, 6, right parenthesis, to the power 8P=141,200(1−0.6) 8
1 answer
To express the population of a town that is shrinking at a rate of 6% per year, we can use the formula for exponential decay:
\[
P = P_0 \times (1 - r)^t
\]
Where:
\( P \) is the population after time \( t \),
\( P_0 \) is the initial population,
\( r \) is the rate of decrease (as a decimal),
\( t \) is the time in years.
In this case:
The initial population \( P_0 = 141,200 \),
The rate of decrease \( r = 0.06 \) (6%),
The time \( t = 8 \) years.
Inserting these values into the formula gives us:
\[
P = 141,200 \times (1 - 0.06)^8
\]
\[
P = 141,200 \times (0.94)^8
\]
Now, looking at the provided multiple-choice answers, the correct representation of the population after 8 years is:
