When Are We Ever Going to Use This?

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Lafayette County Courthouse on the Oxford Mississippi Square Deserted at 10 AM on Tuesday January 17, 2018

Today marks our third consecutive “snow” day.  “Snow” is a misnomer since what kids and people from northern climes consider snow is definitely not what causes us to close schools and other government agencies in Mississippi.  We have extreme weather.  Again, it’s not really extreme if you have the infrastructure to deal with it.  But in Oxford, Mississippi though we do have chilly temperatures, we rarely get debilitating cold/snow/ice.  So, dealing with it is not in our city/county/state budgets.

Yesterday morning we did get some bonafide snow and kids were able to sled.  But as the heat went on and off in our house all afternoon and the temperatures dropped, I began to worry about losing power.  Though we have gas heat, it does not come on without power.  We live in town so we don’t lose power often and thus have never invested in a generator.  We went to bed and it was 7 degrees Fahrenheit.  When we woke up, it was supposed to be 5.

We never went to sleep.  Just as we were about to turn out the last light, it turned itself off and the heater’s comforting sound went whir whir hushhhhhhh.  It was pitch black, like the Little House days.  I couldn’t see anything so I stupidly put my glasses back on.  Guess what?  Still couldn’t see.

Then my husband and I started bumbling around in the dark, searching for flashlights so we could look for the never-used phone book, so we could call the city.  It was clear by peering out our window (exactly the same as the inside of the house — pitch black) that the houses on our cul-de-sac were affected, but was anyone else awake to make the call?  At one point I said, “Use your cell-phone flashlight!”  Duh.  We finally called the emergency line for the electric department and beep-beep-beep-beep-beep.  It was busy.  We weren’t the only ones with a problem.  Our neighbors texted and asked if we were without power and if we had been able to reach the electric department.  Yes.  No.  A few minutes later, one of our calls went through and we left a message.

The kids were in their rooms — the teenager still awake so I offered our bed so we could stay warm while we waited.  “I have a sleeping bag, I’ll zip it up.  Ziiiiiiiiiip,” was all I got.  So then with nothing to do in a pitch black house, my husband and I each did something very much fitting for our personalities. He got in the car and started driving around to see how wide-spread the outage was and whether or not the electric department was already working on it, and I did a math problem.  I did this math problem not as a math teacher but as a mother — I needed to know when and if I would have to move my kids elsewhere to finish out the night.  I did not want to freak out and pull my kids into bed with me.  Except for when your 3-year old runs into a busy street, a parent needs to maintain composure.

When are we ever going to use this?  I got to do the Newton’s Law of Cooling Problem that I have taught for 23+ years!  Here is my version of the story which I will forever use in my calculus classes from now on.

It is 10:50 PM when the power goes out in Ms. Cornelius’ house.  Inside the house the temperature is 65 degrees Fahrenheit, but outside the house it’s 7 degrees.  30 minutes later, still no power, but the house temperature has dropped to 60 degrees.  Should she go to sleep and not worry about freezing children and freezing pipes?  Or should she take the offers of kind friends on social media who have invited her family (and four dogs) to stay with them?

Newton’s Law of Cooling states that a body (in this case our house) will cool at a rate proportional to the difference between it and the ambient air.  Thus, temps will drop (or rise) very quickly with a large difference, but will drop less as the difference decreases.  The model is exponential decay and can be found with a differential equation and a few bits of given information.  Then, the equation can be used as a predictor.  This also works for heating situations like cooking a turkey which is why it always takes so long at the end for the internal temperature of the turkey to reach 165 degrees Fahrenheit with the leg/thigh area reaching 170 degrees.

This is what I did.  I might have a few mistakes in there — let me know in the comments!

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Calculus in real life!

With the given conditions, our house would take about 4.7 hours to reach 32 degrees Fahrenheit.  This made me somewhat relieved and I stopped engaging my teenager in conversation and let the house fall silent.  My husband returned and gave a status report.  The outage was fairly local and they were working on it.  We had a flicker of light and heat and then heard a dull BOOM.  “Dang,” he said, “it’s gonna be more complicated than just flipping a switch.”  He went back out and kept driving around.  I laid there and debated stealing Peanut the chiweenie out of our 9-year old’s bed.

The power DID come back on about 1.7 hours after it first went off.  I fell into a blissfully uninterrupted sleep but I am sure the electrical lineman was off to another call.  THANK YOU to the electrical linemen out in the frigid cold SAVING LIVES, especially of our very young and very old neighbors.

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The exponential model of our house last night — H = 7 + 58e^(-0.1803t) — created in desmos

So the answer to the question, “When are we ever going to use this?” is … the same I always give:  I’m not a fortune teller.  I can’t see into your future.  I’m a math teacher.  I am preparing you for your future.  And now, back to the snow-less snow day.

Click these links to see some differential equations resources I have written.

DE card sort / solve FREE!

DE circuit

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