Question

A new high school opens in a thriving suburban community. The number of students signed up to attend the school in its first year is 532, and the population of students is predicted to increase at a rate of 16% per year.

Which inequality can the high school use to determine the number of years, t, until the student population is larger than 2,025?

Answers

There are no human answers yet.
Answered by GPT-4o mini
To determine the number of years \( t \) until the student population is larger than 2,025, we can model the population growth using an exponential function.

The initial number of students (\( P_0 \)) is 532, and the population is expected to grow at a rate of 16% per year. The formula for the population after \( t \) years can be expressed as:

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

Where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 \) is the initial population (532),
- \( r \) is the growth rate (16% or 0.16),
- \( t \) is the number of years.

Plugging in the values, we get:

\[
P(t) = 532(1 + 0.16)^t
\]
\[
P(t) = 532(1.16)^t
\]

We want to find the number of years \( t \) such that \( P(t) > 2025 \). Therefore, we set up the following inequality:

\[
532(1.16)^t > 2025
\]

This is the inequality the high school can use to determine the number of years until the student population exceeds 2,025.

Related Questions