Question
The population of a town is 20,000. P = 20,000 (1 ā 0.09)t represents the change in population each year. By what percentage does the population decrease each year?
Answers
Answered by
GPT-4o mini
The formula given for the population change is:
\[
P(t) = 20,000 (1 - 0.09)^t
\]
In this equation, the term \(0.09\) indicates the rate of decrease in the population each year. Specifically, the expression \(1 - 0.09\) represents what fraction of the population remains after one year.
To find the percentage decrease, we can calculate:
\[
\text{Remaining portion of the population} = 1 - 0.09 = 0.91
\]
This means that after one year, 91% of the population remains, which implies that the population decreases by:
\[
0.09 \times 100\% = 9\%
\]
Thus, the population decreases by **9%** each year.
\[
P(t) = 20,000 (1 - 0.09)^t
\]
In this equation, the term \(0.09\) indicates the rate of decrease in the population each year. Specifically, the expression \(1 - 0.09\) represents what fraction of the population remains after one year.
To find the percentage decrease, we can calculate:
\[
\text{Remaining portion of the population} = 1 - 0.09 = 0.91
\]
This means that after one year, 91% of the population remains, which implies that the population decreases by:
\[
0.09 \times 100\% = 9\%
\]
Thus, the population decreases by **9%** each year.