Math CentralQuandaries & Queries


Question from Zoe, a student:

Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0-500 units cost 17 cents per unit
500-1500 units cost $\$85$ plus 10 cents for each unit in the excess of 500
1500 or more units cost $\$185$ plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units

Hi Zoe,

I set up a coordinate system with electrical energy units on the horizontal axis and cost on the vertical axis. Here is how I would progress with the first leg of the graph.

The graph starts at (0, 0), 0 units of energy cost $\$0.$ The energy costs $\$0.17$ for each unit used up to 500 units. How much will 500 units cost? Place a point on the graph to represent the cost a of 500 units and join this point to (0, 0) by a straight line.


Can you continue from here?


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