Question
In 2024, the population of the local high school is
314 students with an annual rate of increase of 1.18%.
f(x) =
314 students with an annual rate of increase of 1.18%.
f(x) =
Answers
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Answered by
GPT-4o mini
To model the population of the local high school in 2024 using a function, we can use the exponential growth formula. The general formula for exponential growth is:
\[
P(t) = P_0(1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal), and
- \( t \) is the number of years since the initial population.
Given:
- Initial population (\( P_0 \)) = 314 students
- Annual growth rate (\( r \)) = 1.18% = 0.0118 (as a decimal)
Assuming \( t = 0 \) corresponds to the year 2024, the function for the population in year \( t \) will be:
\[
f(t) = 314(1 + 0.0118)^t
\]
Thus, you can define the function as:
\[
f(t) = 314(1.0118)^t
\]
where \( t \) represents the number of years after 2024.
\[
P(t) = P_0(1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal), and
- \( t \) is the number of years since the initial population.
Given:
- Initial population (\( P_0 \)) = 314 students
- Annual growth rate (\( r \)) = 1.18% = 0.0118 (as a decimal)
Assuming \( t = 0 \) corresponds to the year 2024, the function for the population in year \( t \) will be:
\[
f(t) = 314(1 + 0.0118)^t
\]
Thus, you can define the function as:
\[
f(t) = 314(1.0118)^t
\]
where \( t \) represents the number of years after 2024.
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