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

a class of 24 students is planning a field trip to a science museum. a non - refundable 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 non - refundable 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: Analyze 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 ${s|0\leq s\leq24}$.

Step3: Analyze 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 ${c|50\leq c\leq158}$. Also, since the number of students is a discrete quantity (you can't have a fraction of a student), the graph is discrete.

Answer:

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