Consider the following scenario. The fee for an upcoming science camp is $50 per participant. The total cost of the camp in dollars id 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.

Question

Select all the possible outputs (range values) for the cost function and then explain why you chose those values.
A. 0
B. 50
C. 80
D. 210
E. 150

Answer 1

To determine the possible outputs (range values) for the cost function \( C = 50x \), we first need to understand that \( x \) represents the number of participants, and it cannot be negative. The number of participants must also be a whole number (since you can't have a fraction of a participant).

Given the formula:

• If \( x = 0 \): \( C = 50 \times 0 = 0 \)
• If \( x = 1 \): \( C = 50 \times 1 = 50 \)
• If \( x = 2 \): \( C = 50 \times 2 = 100 \)
• If \( x = 3 \): \( C = 50 \times 3 = 150 \)
• If \( x = 4 \): \( C = 50 \times 4 = 200 \)
• And so on...

The outputs of the function \( C \) are multiples of 50, which means they can be represented as \( 0, 50, 100, 150, 200, \) etc.

Now, let's analyze the options provided: A. 0 - Valid (when \( x = 0 \)) B. 50 - Valid (when \( x = 1 \)) C. 80 - Invalid (not a multiple of 50) D. 210 - Invalid (not a multiple of 50) E. 150 - Valid (when \( x = 3 \))

Based on this reasoning, the valid outputs (range values) for the cost function \( C = 50x \) are A (0), B (50), and E (150).

I chose these values because they correspond to valid inputs (whole non-negative numbers of participants) that result in an output calculated as \( C = 50x \). Values that do not align with this relationship, such as 80 and 210, are excluded from the range.