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

Answer 1

The number of students in the first year is 532. In the second year, this will increase by 16%, which is $532(1.16)$. Each year, another factor of 1.16 will be multiplied. Therefore, the general function will be $532(1.16)^{t-1}$. The inequality that determines until when this is larger than 2025 will be:

$532(1.16)^{t-1} \ \textless \ 2025$