This graph is a pretty literal representation of the cost as described. With no real world context for billing/cost and no mention that the $75 is a continuously rolling cost, I would almost congratulate this student. What I am seeing is a $75 decrease at the beginning of an hour accompanied by a constant amount of money left over until the next hour strikes where a $75 deduction in the bank account happens again. That is my happy take on this. The sad part is that the student almost certainly has been in the presence of this type of problem being solved and those experiences made almost no impression on her/him. On a related note, I sure would like it better if the teacher asked for the generation of the function that represents the amount of money in the bank and then asked the student to graph the function s/he generated.

Michael, this was one of my submissions. Keep up the great work on mathmistakes!

Jim, your comments summarize some of my thinking exactly! I’m not the original author of the problem, but I like your suggestion of a follow-up on the function that represents the amount of money in the bank.

I also wonder if, when this student gets to discrete math / systems, things will suddenly make a lot of sense? ðŸ™‚

I’ve had success with this exact mistake by having students use whiteboards to graph and then compare results. When they see that their slope is opposite everyone else’s, they tend to want to know why. Once they’re curious, they can usually figure it out themselves or have a classmate explain it.