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Net Worth and Melting Ice

Separation of Variables + Differential Equations

In the spring semester of 2017, I was paired with Andre Oliveira to team teach the second semester of an intro calculus sequence. We had a lot of fun coming up with things to do in class. The most fun, for me at least, was coming up with scenarios when we did a mini differential equations module in the class using separation of variables. By the time I'd gotten to this worksheet, we'd come up with a lot of fantastical scenarios to apply what we'd learned. Class often started with a setup phrase that sounded like a prompt for a writing class:

  • "You're a plumber working late at night, when one of the tanks filled with water springs a leak..."

  • "The only forensic scientist in a small town has been murdered, it's up to you to figure out what time the murder occurred."

  • "The owner of a pet shop is looking for a way to increase his sales. You agree to help her out by modelling how fast different types of pets learn to do things. You start with how fast the parrots learn new words."

By the time we got to the worksheet below, my class was expecting an opening that then turned into a story line that moved along with the aid of differential equations. This starts out with helping out on your first day of the job, progresses to asking questions about ice fishing, and comes back around to figuring out when you can become CEO yourself.

A pdf of the worksheet is here, with the solutions I wrote up at the time here. The tex, along with other worksheets, are in this Google drive folder!


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