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Select the correct answer from each drop-down menu.

The function below describes the number of students who enrolled at a university, where [tex]f(t)[/tex] represents the number of students and [tex]t[/tex] represents the time in years.

[tex] f(t) = 18,500(1.03)^t [/tex]

Initially, [tex]$\square$[/tex] students enroll at the university. Every [tex]$\square$[/tex] year(s), the number of students who enroll at the university increases by a factor of [tex]$\square$[/tex].

Sagot :

GinnyAnswer
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.
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