The table shows the linear relationship between the number of loaves of bread produced, x, and the total cost, y, of producing the loaves.
Total Cost of Producing Loaves of Bread
Number of Loaves Produced, x
25
75
Total Cost of Production, y (dollars)
170
210
250
350
400
470
What is the rate of change of the total cost of production with respect to the number of loaves of bread produced?
A $1.25
® $0.80
© $1.60
• $0.70
To find the rate of change of the total cost of production with respect to the number of loaves produced, we can calculate the average rate of change using the given data points.
First, find the change in total cost and the change in number of loaves produced between two consecutive data points:
For the first data point (25 loaves, $170):
Change in total cost = $210 - $170 = $40
Change in number of loaves = 75 - 25 = 50
For the second data point (75 loaves, $210):
Change in total cost = $250 - $210 = $40
Change in number of loaves = 125 - 75 = 50
Now, calculate the average rate of change:
Average rate of change = Change in total cost / Change in number of loaves
= $40 / 50
= $0.80
Therefore, the rate of change of the total cost of production with respect to the number of loaves of bread produced is $0.80.