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08/16/2024 · Elementary School
A town has a population of 5000 and grows at \( 2 \% \) cvery year. What will be the population after 5 years, to the nearest whole number?
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Step-by-step Solution
To calculate the population of the town after 5 years with an annual growth rate of \( 2\% \), we can use the formula for exponential growth:
\[
P = P_0 (1 + r)^t
\]
where:
- \( P \) is the future population,
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the number of years.
Given:
- \( P_0 = 5000 \)
- \( r = 0.02 \) (which is \( 2\% \))
- \( t = 5 \)
Now, substituting the values into the formula:
\[
P = 5000 (1 + 0.02)^5
\]
Calculating \( (1 + 0.02)^5 \):
\[
(1.02)^5 \approx 1.1040808
\]
Now, multiply this by the initial population:
\[
P \approx 5000 \times 1.1040808 \approx 5520.404
\]
Rounding to the nearest whole number, the population after 5 years will be approximately:
\[
\boxed{5520}
\]
Quick Answer
The population after 5 years will be approximately 5520.
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