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

To determine the number of years, t, until the student population is larger than 2,025, we can set up an inequality and solve for t using the growth rate of 16% per year. On solving, we get t = 10 years.

Step-by-step explanation:

To determine the number of years, t, until the student population is larger than 2,025, we can set up the following inequality:

• 532 * (1 + 0.16)^t > 2,025

We use the expression (1 + 0.16)^t to represent the growth rate of 16% per year. Now we can solve for t:

• 532 * (1.16)^t > 2,025

Divide both sides of the inequality by 532:

• (1.16)^t > 2,025/532

• Approximately 3.6030

Take the natural logarithm of both sides:

• t * ln(1.16) > ln(3.6030)

Divide both sides by ln(1.16):

• t > ln(3.6030) / ln(1.16)

• Approximately 10.04

Therefore, it will take approximately 10 years for the student population to be larger than 2,025.

Answer 2

532×1.16ᵗ>2025 is the inequality. The solution of the inequality is t=10 years.