Grade 12: Tire Pressure
You have a hole in your tire. You pump it up to P=400 kilopascals (kPa) and over the next 60 minutes it drops to P = 100. What function describes the P-t graph? A simple physical model of molecules passing randomly through the hole leads us to an exponential decay function.
We then do an actual experiment and collect the data. It does seem to lie along a curve with the predicted concave-up shape.
To check if the data is exponential, we plot log(P) against time. We get a reasonable straight line, and we use that to obtain the percentage rate of decrease of the time pressure.