Too Hot to Handle - Exponential Decay and Translations in Algebra 2

We explored exponential functions in Algebra 2 recently. I had planned on using the NCTM Illuminations lesson: Too Hot to Handle Too Cold to Enjoy since this past summer. However, as I've become more comfortable doing experiments in my classroom and gotten better at creating my own investigations I decided to steal the idea and make it my own.

The setup
Gathering supplies wasn't so difficult--I basically raided various parts of the school:
-stop watches, thermometers, and hot plates from the chemistry room
-coffee mugs and a ladle from the teacher's work room
-and a pot to boil water in from the kitchen.

I wasn't sure how long it would take to boil water on a hotplate so I started it at the end of 2nd period. As it turns out, a pot of water never boils on a hotplate--ever. Over lunch I grabbed another portable stove from the chemistry room in hopes to get the water boiling by 5th period. We gained all of 10 degrees. By the time class rolled around we had 180 degree water.

I introduced the experiment talking about the McDonald's lawsuit back in the 1990's over a elderly lady getting burned by a cup of coffee. We told some stories and ended up discussing that once coffee is 120 degrees, it's cold enough to not scald you and hot enough to still enjoy. I ladled out water to the groups and they set to work collecting temperature data based on the amount of time that had passed since they first started measuring.

Things didn't go well--or at least as well as I had hoped. In the picture below, you can see the tools the students were working with. The thermometer was hard for them to read accurately. As a result, several groups got data that was pretty much linear.

Once the students started in on the process of modeling the data, I had to make a quick decision. I hadn't planned on the data showing up linear and students were asking me what kind of model I wanted. I chose to have them make the model they though best fit their data. Here's some samples of student work.

Here we had a great discussion about how well the model fits the data AND the situation. All but one of my groups went for an exponential decay model. However, all but one of those groups got the model wrong. They did well enough finding growth factors and starting values but they didn't take into account the horizontal asymptote for an exponential decay function; it's always at y=0. This means for all of the above functions, when we made a scatterplot on our calculators and graphed our equation at the same time, the equation went down much faster than the data--even when using exponential regression.

Then the group below presented. They realized the horizontal asymptote needed to be at room temperature so they looked at the thermostat in my room. Then they proceeded to subtract 70 degrees from each of their data points before creating an equation. After finding an equation, they translated the equation back up by 70 degrees. Brilliant!

After one of the groups finished collecting data points, I used their cup of water and my digital thermometer for the graphing calculator to gather some of my own data. Unsurprisingly, it's much easier to tell the difference between temperatures when the water is much hotter. If I was to do this again, I would either want boiling water, better thermometers, a video with a digital thermometer read-out along with the time, or maybe even just the data could work well (but that's on the boring end of things).