Question

Jamilla is moving to a new city. She researches the rates charged by the local unity company for water. She finds the listing rate explanations below. She expects that her family may use up to 1000 cubic feet of water each month.
-$12.70 monthly service fee
-First 300 cubic feet of water used: $3.90 per 100 cubic feet, or fraction thereof
-After the first 300 cubic feet: $5.20 per 100 cubic feet, or fraction thereof

a.) Sketch a graph of the cot of Jamilla's possible water usage in one month. Consider what the cost would be for partial units as 220 or 675 cubic ft of water

Answer 1

We put cubic feet of water used on the x-axis and the cost on the y-axis.
The graph will start at (0 , 12.7) because this is the fees before using any water.
The slope of the graph from 0 < x < 300 will be $0.039/cubic ft, and this interval will start at (0 , 12.7) and end at (300 , 24.4).
The slope of the graph for x > 300 will be $0.052/cubic ft, and this interval will start at (300 , 24.4) and continue to x value infinity.

220 units lies within the interval 0 < x < 300 so we use the first slope.
y = 0.039(220) + 12.57
= $21.15
We break 675 cubic feet into two parts, 300 + 375 cubic feet as they will be charged differently.
The cost of the first 300 cubic feet = $24.40
The cost of the remaining 375 cubic feet = 0.052 x 375 = $19.50
Total cost of 675 cubic feet = $43.90