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):
-
0
- Reason: It is possible to have zero participants. In this case, the total cost would also be zero, which makes logical sense.
-
25
- Reason: This is a valid number of participants, and it results in a total cost of $1250 (i.e., \( C = 50 \times 25 \)).
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50
- Reason: A scenario with 50 participants is plausible. It would result in a total cost of $2500 (i.e., \( C = 50 \times 50 \)).
-
100
- Reason: Having 100 participants is also valid, leading to a total cost of $5000 (i.e., \( C = 50 \times 100 \)).
Invalid Inputs:
-
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.
-
-20
- Reason: Negative participant counts are not feasible in this scenario. You cannot have a negative number of participants.
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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.