Question

1. the number of students enrolled at a certain university increases by 3% each year. in 2010, the university has 27, 360 students enrolled. write an equation for a function n, where n(t) models the number of enrollments per year and t is the time in years since 2010.

Explanation:

Step1: Identify the type of growth

This is exponential growth. The general formula for exponential growth is \( n(t) = n_0(1 + r)^t \), where \( n_0 \) is the initial amount, \( r \) is the growth rate, and \( t \) is time.

Step2: Determine the values of \( n_0 \) and \( r \)

The initial number of students \( n_0 \) in 2010 is 27,360. The growth rate \( r \) is 3% or 0.03.

Step3: Substitute the values into the formula

Substituting \( n_0 = 27360 \) and \( r = 0.03 \) into the exponential growth formula, we get \( n(t) = 27360(1 + 0.03)^t \), which simplifies to \( n(t) = 27360(1.03)^t \).

Answer:

\( n(t) = 27360(1.03)^t \)