a class of 24 students is planning a field trip to a science museum. a nonrefundable deposit of $50 is…

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.

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.

Answer

Explanation:

Step1: Determine the linear - function formula

The fixed deposit is $50$ and the cost per student is $4.50$. So the cost $c$ as a function of the number of students $s$ is $c = f(s)=4.5s + 50$.

Step2: Find the domain

The number of students $s$ can range from $0$ to $24$ (since there are 24 students in the class). So the domain is ${s|0\leq s\leq24}$ (using $s$ as the variable for the number of students).

Step3: Find the range

When $s = 0$, $c=f(0)=4.5\times0 + 50=50$. When $s = 24$, $c=f(24)=4.5\times24+50=108 + 50=158$. So the range is ${c|50\leq c\leq158}$.

Step4: Analyze the graph

Since the number of students $s$ can only take on whole - number values (you can't have a fraction of a student), the graph is discrete, not continuous.

Answer:

The linear model is $f(s)=4.5s + 50$. The domain is ${x|0\leq x\leq24}$. The range is ${y|50\leq y\leq158}$.