Real-Life Math
You are an engineer who examines patents that have something to do with temperature. Your area of specialty is consumer products.
This means you see patent applications for things like a hair dryer or air conditioner. Often, when inventors spot a trend, many of them apply for patents that are so similar they could be identical.
This month, you have received 3 applications for lunch boxes that claim to keep your lunch hotter than anyone else's lunch box. Before you can check the patent archives for "prior art" (that is, check to see if someone else already has a patent on it), you must first determine if these lunch boxes do what they claim they do.
"I encounter mathematics in at least half of the applications I see," says patent examiner Leo Boudreau.
Since "hot" food means different things to different people, you need to set up a controlled method of determining what "hot" is. First, you decide to heat the "food." In this case, it is 8 oz. of water heated to 100 degrees F.
Then you place temperature probes in each lunch box to monitor the decline in temperature over 4 hours. After the tests are complete, you discover some very interesting data. All 3 lunch boxes lost about the same amount of heat overall, but they lost it in much different ways.
You struggle to find a way to compare them. This is a challenge because the water is as cold in all 3 at the end of the 4 hours. Surely, one lunch box truly does do a better job.
Finally, you decide to graph the data. Here is the key data:
Lunch box A lost 10 degrees in the first hour, none for the next 2 hours and then 20 more degrees in the last hour.
Lunch box B lost heat steadily at 7.5 degrees per hour.
Lunch box C lost all the heat it was going to lose in the first hour and kept the temperature steady at 70 degrees for 3 more hours.
We recommend a line graph.