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)

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

(3 points)
Responses

-20
-20

25
25

10.5
10.5

0
0

50 3/4
50 3/4

100

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

In the scenario given, the cost function is defined as \( C = 50x \), where \( x \) represents the number of participants. Here are the considerations for the possible inputs (domain values) for this function:

  1. -20: Not a valid input. You cannot have a negative number of participants.

  2. 25: Valid input. This represents 25 participants, leading to a total cost of \( C = 50 \times 25 = 1250 \).

  3. 10.5: Not a valid input. Participants must be a whole number; you cannot have half a participant.

  4. 0: Valid input. This represents a scenario where there are no participants, resulting in a cost of \( C = 50 \times 0 = 0 \).

  5. 50 3/4: Not a valid input. Similar to 10.5, you cannot have a fraction of a participant.

  6. 100: Valid input. This represents 100 participants, leading to a total cost of \( C = 50 \times 100 = 5000 \).

Summary of Selected Values:

  • Valid inputs (domain values) for this scenario are 0, 25, and 100.
  • I chose these values because:
    • The input must be a non-negative integer (whole number) since you cannot have a negative number of participants or a fraction of a participant in this context.
    • Hence, values like -20, 10.5, and 50 3/4 are not possible. Only whole numbers greater than or equal to zero are acceptable as inputs for the function.