Bob 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.

Question

There is a linear relationship between the number of bags of recyclables and the total cost of the service.
Number of bags Total cost
0 $10.00
2 $17.00
4 $24.00
Describe the rate of change for this relationship.
The total cost of the recycling service
by
per bag.

Answer 1

To determine 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 points.

From the data:

• When there are 0 bags, the total cost is $10.00.
• When there are 2 bags, the total cost is $17.00.
• When there are 4 bags, the total cost is $24.00.

We can calculate the cost per bag for the linear change between the total cost and the number of bags.

1. Calculate the difference in cost between 0 bags and 2 bags: \[ \text{Cost increase from 0 to 2 bags} = 17 - 10 = 7 \text{ dollars} \] \[ \text{Number of bags} = 2 - 0 = 2 \] \[ \text{Cost per bag} = \frac{7}{2} = 3.50 \text{ dollars per bag} \]

2. Calculate the difference in cost between 2 bags and 4 bags: \[ \text{Cost increase from 2 to 4 bags} = 24 - 17 = 7 \text{ dollars} \] \[ \text{Number of bags} = 4 - 2 = 2 \] \[ \text{Cost per bag} = \frac{7}{2} = 3.50 \text{ dollars per bag} \]

From both intervals, we can see that the cost per bag remains constant at $3.50.

Summary:

The total cost of the recycling service increases by $3.50 per bag.