Answer:
[tex]f(t)=120+18t[/tex]
Explanation:
We know that for the initial year of a summer camp, 56 girls and 64 boys enrolled.
The total children enrolled for the initial year can be calculated as :
[tex]56+64=120[/tex]
Each year, 18 more students enrolled in the camp.
The variable ''[tex]t[/tex]'' represents the time in years since the camp opened.
The following expression :
[tex]18t[/tex]
represents the extra children enrolled each year
If we sum, we can obtain the following expression :
[tex]120+18t[/tex]
which is the function [tex]f(t)[/tex] for the total number of students enrolled [tex]t[/tex] years after the camp opened.
The function rule is [tex]f(t)=120+18t[/tex]
For example, when [tex]t=0[/tex] ⇒
[tex]f(0)=120+18(0)=120[/tex]
which is the original amount of enrolled children when the summer camp opened.
When [tex]t=3[/tex] ⇒
[tex]f(3)=120+18(3)=174[/tex]
which is the expected value for the total number of students enrolled 3 years after the camp opened.
