Question

For the initial year of a summer camp, 56 girls and 64 boys enrolled. Each year thereafter, 18 more students enrolled in the camp. Let t be the time (in years) since the camp opened. Part A: Write a function rule for the total number of students enrolled t years after the camp opened.

Answer 1

`f(t)=120+18t`

Step-by-step 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 :

`56+64=120`

Each year, 18 more students enrolled in the camp.

The variable ''
`t`'' represents the time in years since the camp opened.

The following expression :

`18t`

represents the extra children enrolled each year

If we sum, we can obtain the following expression :

`120+18t`

which is the function
`f(t)` for the total number of students enrolled
`t` years after the camp opened.

The function rule is
`f(t)=120+18t`

For example, when
`t=0` ⇒

`f(0)=120+18(0)=120`

which is the original amount of enrolled children when the summer camp opened.

When
`t=3` ⇒

`f(3)=120+18(3)=174`

which is the expected value for the total number of students enrolled 3 years after the camp opened.