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Answer :
To describe the rate of change for the relationship between the area of the floor (in square feet) and the total cost, we need to determine how much the cost changes for each additional square foot of flooring.
Here's a step-by-step explanation:
1. Identify Two Data Points:
Let's select two of the given data points to calculate the rate of change. For instance, we can use:
- Point 1: (50 square feet, [tex]$200)
- Point 2: (100 square feet, $[/tex]400)
2. Calculate the Change in Total Cost:
Find the difference in total cost between the two points.
[tex]\[
\text{Change in Cost} = \$400 - \$200 = \$200
\][/tex]
3. Calculate the Change in Area:
Find the difference in the area (in square feet) between the two points.
[tex]\[
\text{Change in Area} = 100 \, \text{square feet} - 50 \, \text{square feet} = 50 \, \text{square feet}
\][/tex]
4. Determine the Rate of Change:
The rate of change is calculated by dividing the change in total cost by the change in area.
[tex]\[
\text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Area}} = \frac{\$200}{50 \, \text{square feet}} = \$4.00 \, \text{per square foot}
\][/tex]
Therefore, the total cost increases by $4.00 per square foot.
Here's a step-by-step explanation:
1. Identify Two Data Points:
Let's select two of the given data points to calculate the rate of change. For instance, we can use:
- Point 1: (50 square feet, [tex]$200)
- Point 2: (100 square feet, $[/tex]400)
2. Calculate the Change in Total Cost:
Find the difference in total cost between the two points.
[tex]\[
\text{Change in Cost} = \$400 - \$200 = \$200
\][/tex]
3. Calculate the Change in Area:
Find the difference in the area (in square feet) between the two points.
[tex]\[
\text{Change in Area} = 100 \, \text{square feet} - 50 \, \text{square feet} = 50 \, \text{square feet}
\][/tex]
4. Determine the Rate of Change:
The rate of change is calculated by dividing the change in total cost by the change in area.
[tex]\[
\text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Area}} = \frac{\$200}{50 \, \text{square feet}} = \$4.00 \, \text{per square foot}
\][/tex]
Therefore, the total cost increases by $4.00 per square foot.
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