Sure, let's break this down step-by-step.
Given the function:
[tex]$
f(t) = 18,500(1.03)^t
$[/tex]
1. Interpreting the Initial Enrollment:
- Initially, or when [tex]\( t = 0 \)[/tex], we need to identify the initial number of students enrolled.
- For [tex]\( t = 0 \)[/tex]:
[tex]$
f(0) = 18,500 \times (1.03)^0 = 18,500 \times 1 = 18,500
$[/tex]
- Thus, initially, [tex]\( 18,500 \)[/tex] students enrolled at the university.
2. Interpreting the Time Period:
- The variable [tex]\( t \)[/tex] represents time in years.
- This means that we are considering the number of students enrolling per year.
3. Interpreting the Growth Factor:
- The factor [tex]\( 1.03 \)[/tex] is used in the function, which indicates that every year the number of students increases by multiplying the previous year's number of students by [tex]\( 1.03 \)[/tex].
- This suggests that every year, the number of students increases by a factor of [tex]\( 1.03 \)[/tex].
Therefore, with these interpretations, the correct choices from the drop-down menus are:
- Initially: [tex]\( 18,500 \)[/tex] students enroll at the university.
- Every: year.
- The number of students who enroll at the university increases by a factor of: [tex]\( 1.03 \)[/tex].
So, the filled statements are:
Initially, 18,500 students enroll at the university. Every year, the number of students who enroll at the university increases by a factor of 1.03.
