Some carpet cleaning costs are 1 room for $125, 2 rooms for $175, 3 rooms for $225. and 4 rooms for $275.00.find and interpret the rate of change and the initial value for this situation.

First calculate the hourly rate, which is the difference of cleaning 2 and 1 rooms:
175-125=50

then calculate the initial value by subtracting the hourly rate from the "1 room" cost:
125-50=75

The initial cost might be something like driving to the place (which is only necessary once), while the rate covers work time or cleaning utensils used.