High School

Bridget is starting a home renovation project and wants to determine how many rooms she can update with new flooring while staying within her budget. She calculates the costs based on the square footage of each room.

There is a linear relationship between the area of the floor, in square feet, and the total cost.

[tex]
\[
\begin{tabular}{|c|c|}
\hline
\text{Area of floor (square feet)} & \text{Total cost} \\
\hline
50 & \$200.00 \\
\hline
100 & \$400.00 \\
\hline
150 & \$600.00 \\
\hline
200 & \$800.00 \\
\hline
\end{tabular}
\]
[/tex]

Describe the rate of change for this relationship.

The total cost increases by \$4.00 per square foot.

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.

Other Questions