Question

writing a linear function to model a real - world scenario
a class of 24 students is planning a field trip to a science museum a nonrefundable deposit of $50 is required for the day - long program, plus a charge of $4.50 per student.
determine a linear function that models the cost, c, and the number of students, s.
which statements about the linear function and its graph are correct? check all that apply
□ the linear model is f(s)=4.5s + 50
□ the linear model is f(c)=54.5c + 24
□ the domain is {x|0≤x≤24}
□ the range is {y|50≤y≤158}
□ the graph is continuous

Explanation:

Step1: Define linear function

The total cost $c$ (or $f(s)$) is the nonrefundable deposit plus per-student cost. The deposit is $50, per student cost is $4.50, so:
$f(s) = 4.5s + 50$

Step2: Identify valid domain

Number of students $s$ is between 0 and 24 (inclusive, since it's a class of 24). Domain: $\{x \mid 0 \leq x \leq 24\}$ (using $x$ for $s$ as in the option).

Step3: Calculate valid range

Substitute $s=0$: $f(0)=4.5(0)+50=50$
Substitute $s=24$: $f(24)=4.5(24)+50=108+50=158$
Range: $\{y \mid 50 \leq y \leq 158\}$

Step4: Check graph continuity

Number of students is a whole number, so the graph is discrete (not continuous).

Answer:

• The linear model is $f(s) = 4.5s + 50$
• The domain is $\{x \mid 0 \leq x \leq 24\}$
• The range is $\{y \mid 50 \leq y \leq 158\}$