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 the number of students (x) and your output is the total cost (C)

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

(3 points)
Responses

210
210

50
50

80
80

0
0

150

1 answer

To determine the possible outputs (range values) for the cost function \( C = 50x \), we need to analyze the relationship between the number of participants \( x \) and the total cost \( C \).

  1. Understanding the Function:

    • The function \( C = 50x \) indicates that for every participant (x), the cost increases by $50.
    • Therefore, if there are zero participants, the cost is $0 (C = 50 * 0 = 0).
    • If there is one participant, the cost is $50 (C = 50 * 1 = 50).
    • If there are two participants, the cost is $100 (C = 50 * 2 = 100).
    • This pattern continues such that the total cost is always a multiple of $50 depending on the number of participants.
  2. Selecting the Possible Outputs:

    • The possible outputs must be non-negative since the cost cannot be negative. Hence, \( C \) can be 0 (if there are zero participants).
    • As for other outputs:
      • \( 50 \) is a possible output when there is 1 participant.
      • \( 80 \) is not a possible output, because it is not a multiple of 50.
      • \( 150 \) is a possible output when there are 3 participants (C = 50 * 3).
      • \( 210 \) is not a possible output, since it is also not a multiple of 50.
  3. Conclusion: Based on this analysis, the possible outputs from the given options are:

  • 0
  • 50
  • 150

These outputs are valid because they correspond to the total costs generated by integer values of \( x \) that result in non-negative multiples of 50. Thus, the selected possible outputs (0, 50, 150) reflect the outputs generated from valid integer inputs into the cost function.