Question

4. The cost of a history club trip includes $78 for transportation rental plus a $2 admission charge for each student participating. The total cost of the trip depends on the number of students participating. All 52 history club students plan on participating.a. Identify the input and output variables.b. Write a function rule that expresses the total cost, C, as a function of the number of students, s.c. What is the practical domain of the total cost function?d. What is the practical range of the total cost function?

Answer 1

a)

You have two variables

"Cost of history club trip"

"Number of students participating in the trip"

The independent variable will be the one that produces significant changes in the second one, in this case, we know that the cost of the trip varies with the number of students atending.

So the independent variable or input will be "Number of students participating in the trip" and the dependent variable or output will be "Cost of history club trip"

b)

To write the function you have to determine how much the Cost changes when the number of participants increase in one unit.

The cost per student is $78 + $2= $80, this means that each time a student confirms the trip, the cost increases $80, as a function it is:

C=$80*S

c)

The domain of the function represents all possible values for the input, or x variable.

You have to leave the zero behind since it would not be practical to calculate the cost of a trip that no student will participate in, then the domain of the function will be between 1 (minimum quantity of students) and 52 (total number of students)

Domain: 1 ≤x≤52

c) The range of the function are all possible values for the output, or dependent variable. Its minimum value will be if only one student goes to the trip: C=$80*1=$80

And its maximum value will be the cost of the trip if all students go to the trip:

C=$80*52=$4160

So the range of the function will be

$80≤y≤$4160