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 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

0
0

150
150

210
210

80
80

50

GPT-4o mini · Answer

In the scenario given, the cost function is expressed as $C = 50 x$ , where $x$ represents the number of participants. Since $x$ must be a non-negative integer (you cannot have a negative number of participants), the possible outputs (C) for the function can be determined by multiplying 50 by non-negative integers.

For $x = 0$ (no participants), the total cost $C = 50 \cdot 0 = 0$ .
For $x = 1$ (1 participant), $C = 50 \cdot 1 = 50$ .
For $x = 2$ (2 participants), $C = 50 \cdot 2 = 100$ .
For $x = 3$ (3 participants), $C = 50 \cdot 3 = 150$ .
For $x = 4$ (4 participants), $C = 50 \cdot 4 = 200$ .
For $x = 5$ (5 participants), $C = 50 \cdot 5 = 250$ .
And so on...

The possible outputs will include all multiples of 50 (0, 50, 100, 150, 200, etc.).

Now, evaluating the choices provided:

0: Yes, because when there are no participants, the total cost is $0.
50: Yes, because with one participant, the total cost is $50.
150: Yes, because with three participants, the total cost is $150.
80: No, because 80 is not a multiple of 50.
210: No, because 210 is not a multiple of 50.

Chosen Outputs (Range Values):
0, 50, 150

Explanation: These values are the results of multiplying the participant numbers (0, 1, and 3) by the fee of $50. Other non-multiples of 50, such as 80 and 210, are not possible outputs for this cost function. All valid outputs must reflect the camp cost based on the number of participants, which is constrained to increments of $50.