Mathematizing

=How hot does your car get?= Math teachers often say that math can be applied to many things in real life, but what are some examples? After watching a video on YouTube talking about the temperature in a car on a warm day and its effect on pets, I thought it would be interesting to see if there is a mathematical model for the increase in temperature over time. media type="custom" key="23446642"

I set up a temperature probe inside thecar, which was connected to a computer that recorded the temperature every minute for 2 hours. The data are shown below (the car temperature data is in blue, the temperature outside is in pink and is from NOAA's records.) I then used [|this website] to run a regression on the data. The graph looks like a power function to me, so that is what I used. The regression software suggested that an appropriate model would be y = 21.24(x) 0.127 I graphed this equation in green as shown below, and I think it makes a pretty nice model:

What does this data mean? First of all, we see that there was a huge difference between the outside temperature and the temperature inside the car. While the temperature outdoors didn't get past 23.9 C (75 F), the temperature in the car got to about 39.5 C (103 F). More importantly, we see that the greatest increase in temperature occurs within the first 30 minutes or so of parking the car. What this data suggests to me is that there really is no "safe" amount of time to leave a pet in the car in the summer, especially since this was a mild summer day.