Question

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 10.5 10.5 0 0 25 25 -20 -20 100 100 50 3450 34

Answer 1

To determine the possible inputs (domain values) for the cost function \( C = 50x \), where \( x \) represents the number of participants, we need to consider what constitutes a valid number of participants in the context of this scenario.

1. **Non-negative integers**: The number of participants must be a non-negative integer because it doesn't make sense to have a fraction of a participant or a negative number of participants. Therefore, any valid input must be a whole number greater than or equal to 0.

Based on this criterion, let’s evaluate the provided options:

- **10.5**: Not a valid input (not an integer).
- **0**: Valid input (0 participants).
- **25**: Valid input (25 participants).
- **-20**: Not a valid input (negative participants).
- **100**: Valid input (100 participants).
- **50**: Valid input (50 participants).
- **3450**: Valid input (3450 participants).
- **34**: Valid input (34 participants).

From the list, the valid inputs for the cost function are: **0, 25, 100, 50, 3450, 34**.

### Summary of Accepted Domain Values:
- **0**: Represents no participants.
- **25**: Represents a normal size group.
- **100**: Represents a larger group.
- **50**: Represents a smaller standard group.
- **3450**: Represents an extremely large group, though it's feasible.
- **34**: Represents another reasonable group size.

### excluded values:
- **10.5 and -20**: Excluded because they do not meet the criteria of being non-negative whole numbers.

In conclusion, the possible inputs for the cost function are non-negative integers, as you cannot have fractional or negative participants in this context.