Many other similar situations could be quoted to you. Rate of change really is often found in practical, everyday problems. Many of these jobs pay well and are very enjoyable. I think it has to do with measurement. I love it when people really think about what is going on.
Measurement is certainly a major contribution of math to the many areas of science.
Not just length measurements, either, but also time, velocity, quanitity, volume, and even probability. Math helps scientists and engineers use measurements they have made on certain areas of their systems to calculate other measurements they have not made but want to know. The distance divided by the time gave the speed of light. This is a very important part of it to me, as that is what I do. I would like to use from the model.