Question
Felipe lives in a town that doesn't have a recycling program. Instead, his family pays for a recycling service. They paid an initial fee to get access to the service and an additional fee per bag of recyclables. There is a linear relationship between the number of bags of recyclables and the total cost of the service. 5 10 15 20 25 30 35 40 45 50 55 60 $5 $10 $15 $20 $25 $30 $35 $40 $45 $50 $55 $60 x y Number of bags Total cost ($) Describe the rate of change for this relationship. The total cost of the recycling service increases decreases by $3.50 $4.50 $7.00 $10.00 $35.00 $45.00 per bag.
Answers
GPT-4o mini
To find the rate of change for the relationship between the number of bags of recyclables and the total cost of the service, we can analyze the provided data.
From the data table, we see the following pairs of values:
- 5 bags: $10
- 10 bags: $20
- 15 bags: $30
- 20 bags: $40
- 25 bags: $50
- 30 bags: $60
The linear relationship indicates that for each additional bag of recyclables, the total cost increases by a consistent amount.
To determine the rate of change, we can calculate the change in total cost per change in the number of bags:
From the data:
- From 0 bags to 5 bags: Cost changes from $0 to $10 → Change in cost = $10 - $0 = $10; Change in bags = 5 - 0 = 5. Rate of change = 10 / 5 = $2 per bag.
This is consistent for each interval:
- From 5 to 10 bags: Cost changes from $10 to $20 → Change in cost = $20 - $10 = $10; Change in bags = 5 - 0 = 5. Rate of change = 10 / 5 = $2 per bag.
Continuing with this approach, you find that regardless of the interval chosen, the rate of change remains constant at $2 per bag.
Therefore, the answer is:
The total cost of the recycling service **increases by $2 per bag**.
From the data table, we see the following pairs of values:
- 5 bags: $10
- 10 bags: $20
- 15 bags: $30
- 20 bags: $40
- 25 bags: $50
- 30 bags: $60
The linear relationship indicates that for each additional bag of recyclables, the total cost increases by a consistent amount.
To determine the rate of change, we can calculate the change in total cost per change in the number of bags:
From the data:
- From 0 bags to 5 bags: Cost changes from $0 to $10 → Change in cost = $10 - $0 = $10; Change in bags = 5 - 0 = 5. Rate of change = 10 / 5 = $2 per bag.
This is consistent for each interval:
- From 5 to 10 bags: Cost changes from $10 to $20 → Change in cost = $20 - $10 = $10; Change in bags = 5 - 0 = 5. Rate of change = 10 / 5 = $2 per bag.
Continuing with this approach, you find that regardless of the interval chosen, the rate of change remains constant at $2 per bag.
Therefore, the answer is:
The total cost of the recycling service **increases by $2 per bag**.