Question

Brenda is excited for the winter season! She purchased a season pass at Snow Day Ski Resort and plans to ski most days. However, this year she also wants to try snowboarding. Since she doesn't own a snowboard, she will need to rent the equipment. There is a linear relationship between the number of days Brenda rents snowboard equipment, and the total cost of her season. 1 2 3 4 5 6 7 8 9 10 11 12 $100 $200 $300 $400 $500 $600 $700 $800 $900 $1,000 $1,100 $1,200 x y Number of days Brenda rents equipment Total cost ($) Describe the rate of change for this relationship. The total cost increases decreases by $25.00 $40.00 $60.00 $300.00 $600.00 $900.00 per day Brenda rents equipment.

Answer 1

To determine the rate of change for the relationship between the number of days Brenda rents snowboard equipment and the total cost, we can analyze the given data:

- The number of days Brenda rents equipment is represented by \( x \), and the total cost is represented by \( y \).
- The values of \( y \) (total cost in dollars) increase linearly as \( x \) (number of days) increases from 1 to 12 days.

From the data provided:
- On day 1, the cost is $100.
- On day 2, the cost is $200.

Continuing this pattern, we see that each day the cost increases by $100 from the previous day. Let's summarize it:

- When \( x = 1 \), \( y = 100 \)
- When \( x = 2 \), \( y = 200 \)
- When \( x = 3 \), \( y = 300 \)
- When \( x = 4 \), \( y = 400 \)
- ...

This is a linear relationship, and we can find the rate of change (slope) by calculating the change in \( y \) divided by the change in \( x \):

\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{200 - 100}{2 - 1} = \frac{100}{1} = 100
\]

So the total cost increases by **$100.00** for each day Brenda rents the equipment.

Thus, the correct statement is: "The total cost increases by $100.00 per day Brenda rents equipment."