A: The function is decreasing at a decreasing rate (that is, the changes are negative and growing in size). B: The function is decreasing at a constant rate. C: The function is decreasing at an increasing rate (that is, the changes are negative but becoming smaller in size). D: The function is increasing at a decreasing rate (that is, the changes are positive but shrinking).

Did you know that the concept of rates of change is a cornerstone of calculus? It helps us understand how functions behave, especially when they aren't just straightforward increases or decreases! For instance, a decreasing function at a decreasing rate might resemble a car slowing down smoothly, while a function decreasing at a constant rate could be like a train chugging along steadily without speed fluctuations. Speaking of functions, they have real-world applications everywhere — from physics to economics! For instance, understanding how a company's revenue changes over time can help forecast future profits. If the revenue is decreasing at an increasing rate, businesses can identify and address issues quickly to avoid going off the rails before they face bigger problems!