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: 120, 140, 160, 180.
Total cost (dollars): 840, 980, 1120, 1260.
A. $7 per square foot
B. $14 per square foot
C. $28 per square foot
D. $70 per square foot
B. $14 per square foot
To find the rate of change, we can subtract the total cost for the initial number of square feet from the total cost for the final number of square feet, and then divide by the change in the number of square feet purchased.
Rate of change = (Total cost for final number of square feet - Total cost for initial number of square feet) / (Final number of square feet - Initial number of square feet)
Using the data:
Rate of change = (1260 - 840) / (180 - 120)
Rate of change = 420 / 60
Rate of change = 7
Therefore, the rate of change of the total cost in dollars with respect to the number of square feet purchased is $7 per square foot.