#24.
The table shows the total cost of different numbers of square feet of carpet. What is the rate of change of the total cost in dollars with respect to the number of square feet purchased for this linear relationship?
Number of Square Feet Purchased
Total Cost (dollars)
Number of Square Feet Purchased Total Cost (dollars)
100 300
200 600
300 900
To find the rate of change of the total cost with respect to the number of square feet purchased, we need to find the slope of the linear relationship between the two variables.
First, we calculate the change in total cost:
Change in total cost = 900 - 300 = 600
Next, we calculate the change in number of square feet:
Change in number of square feet = 300 - 100 = 200
Now, we can find the rate of change (slope) as:
Rate of change = Change in total cost / Change in number of square feet
Rate of change = 600 / 200 = 3
Therefore, the rate of change of the total cost in dollars with respect to the number of square feet purchased for this linear relationship is $3 per square foot.