I recommend to stick to kinematic motion as the initial, most common application. "How fast the car goes." It is just the easiest to understand from daily life (even if you are a nurse, not an engineer/physicist). Of course there are many other functions (thermal, financial, etc.) But a lot of these are more abstract ESPECIALLY if time is NOT the independent variable.
Remember for weaker students, don't get too tricky at first. While all the regulars here are good at math, you need to consider your audience is not them, but your actual students. Practical pedagogy--not "interesting". In particular, an easy example to stay away from is the Joel's area example--too abstract for new, weak, students. (Not to go after Joel but to make an example of what not to do.)
Finally, this question shows a lack of any initial effort. I would say this to a student asking for homework help. But a teacher? Can't you at least scan a couple textbooks? Do a 1 minute Google search? We can help you better (and you help yourself more also) if you make some small initial effort yourself.