Consider the following scenario.

Question

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)

1. Select all the possible Inputs (Domain values) for the cost function, and then explain why you chose those values.

(3 points)
Responses

10.5
10.5

0
0

100
100

50 34
50 34

-20
-20

25

Answer 1

To identify the possible inputs (domain values) for the cost function \( C = 50x \), we need to consider the context of the scenario, which involves the number of participants (students) attending a science camp.

Possible Inputs (Domain Values):

1. 0

   • Reason: It is possible to have zero participants. In this case, the total cost would also be zero, which makes logical sense.

2. 25

   • Reason: This is a valid number of participants, and it results in a total cost of $1250 (i.e., \( C = 50 \times 25 \)).

3. 50

   • Reason: A scenario with 50 participants is plausible. It would result in a total cost of $2500 (i.e., \( C = 50 \times 50 \)).

4. 100

   • Reason: Having 100 participants is also valid, leading to a total cost of $5000 (i.e., \( C = 50 \times 100 \)).

Invalid Inputs:

1. 10.5

   • Reason: This value is not valid because the number of participants must be a whole number. You cannot have half a participant in this context.

2. -20

   • Reason: Negative participant counts are not feasible in this scenario. You cannot have a negative number of participants.

3. 50 34

   • Reason: This is not a single valid number. It appears to be misformatted and does not represent a valid input for the number of participants.

Summary:

The valid inputs (domain values) for the cost function \( C = 50x \) are whole numbers greater than or equal to 0 (i.e., \( 0, 25, 50, 100 \)). Values like fractions, negative numbers, or improperly formatted numbers are not acceptable in this context.