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

Answer:

$f(t)=120+18t$

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.