Consider the following scenario. The fee for an upcoming science camp is $50 per participant the total cost of the camp in dollars is a function of the number of participants c=50x where your input is number of students (x) and your output is the total cost(c)

Question

Select all the possible inputs (domain values) for the cost function and then explain why you chose those values
A. 25
B. 10.5
C. -20
D. 50 3/4
E. 100
F. 0

Answer 1

To determine the possible inputs (domain values) for the cost function \( c = 50x \), where \( x \) represents the number of participants in the science camp, we need to consider the context of the problem. The number of participants must be a non-negative integer since you cannot have a negative number of participants or a fractional count of participants. Let's evaluate each option:

A. 25 - This is a valid input because it is a non-negative integer.

B. 10.5 - This is not a valid input because the number of participants must be a whole number (integer).

C. -20 - This is not a valid input because the number of participants cannot be negative.

D. 50 3/4 (or 50.75) - This is not a valid input because, like option B, the number of participants must be a whole number.

E. 100 - This is a valid input because it is a non-negative integer.

F. 0 - This is a valid input because it is a non-negative integer, representing a scenario where no participants are enrolled.

Summary of Valid Inputs:

• Valid inputs (or domain values) for the cost function are: A (25), E (100), and F (0).

Reasoning:

I chose these values because the number of participants, \( x \), must be a non-negative integer. Participants cannot be negative or fractional, which eliminates options B, C, and D from the valid set of inputs.