Compound interest is a common example. If you have interest of 5% for every unit of time t, for example, then your total follows an exponential function:
Total = 1.05^t
As t increases, the total increases faster and faster. That's important because it means what seems like a small amount of debt (or a modest investment) can snowball quite drastically over time; it's better to pay off debts as early as possible, and to leave investments as long as possible.