Question

angie works at the park city ice rinks snack stand. at the beginning of her shift today, she made 300 cups of popcorn. each serving angie sells during her shift contains 3 cups of popcorn. the function c(p) represents how many cups of popcorn remain in the machine after angie sells p servings.
what is the range of c(p)?
all multiples of 3 from 0 to 300
all multiples of 3 greater than or equal to 300
all real numbers less than or equal to 100
all real numbers less than or equal to 300

Explanation:

Step1: Define the function

First, write the function for remaining popcorn. Initial cups are 300, each serving uses 3 cups. So:
$C(p) = 300 - 3p$

Step2: Find valid domain of $p$

$p$ is the number of servings, so $p \geq 0$. When no popcorn is left, $300 - 3p = 0$, so $p = 100$. Thus $0 \leq p \leq 100$, where $p$ is an integer.

Step3: Determine range values

Substitute valid $p$ values:

• When $p=0$, $C(0)=300$
• When $p=1$, $C(1)=297$
• ...
• When $p=100$, $C(100)=0$

All results are multiples of 3 between 0 and 300.

Answer:

all multiples of 3 from 0 to 300