Question

At the farmer's market there is someone selling spices. There is a cost to buy the jar that holds the spices, then there is a cost per ounce of spices. The table represents the graph that displays this relationship between total cost and ounces of spices you buy. Ounces Total Cost 0 $5.00 2 $14.00 4 $23.00 10 $50.00

Answer 1

To analyze the cost structure from the data you provided, we can break down the components of the total cost into two parts:

1. The fixed cost of the jar.
2. The variable cost based on the number of ounces of spices.

From the table:

• At 0 ounces, the total cost is $5.00. This likely represents the fixed cost of the jar.
• As you buy more ounces of spices, the total cost increases.

Let's calculate the cost per ounce of spice using the data points:

1. For 2 ounces: \[ \text{Total cost} = $14.00 \] \[ \text{Cost of spices} = $14.00 - $5.00 = $9.00 \] \[ \text{Cost per ounce} = \frac{9.00}{2} = $4.50 \]

2. For 4 ounces: \[ \text{Total cost} = $23.00 \] \[ \text{Cost of spices} = $23.00 - $5.00 = $18.00 \] \[ \text{Cost per ounce} = \frac{18.00}{4} = $4.50 \]

3. For 10 ounces: \[ \text{Total cost} = $50.00 \] \[ \text{Cost of spices} = $50.00 - $5.00 = $45.00 \] \[ \text{Cost per ounce} = \frac{45.00}{10} = $4.50 \]

From your data, we can conclude:

• The fixed cost of the jar is $5.00.
• The cost per ounce of spices is $4.50.

If you want to express the total cost \( C \) as a function of ounces \( x \) of spices, it would be: \[ C(x) = 5 + 4.5x \]

This equation can be used to calculate the total cost for any number of ounces of spices.