Abba Tossou kanem
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Monday 05 October 2026 11:59:00 GMT
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![Math time with Pompompurin! If we let y = f(x) = f(t) be a function, then the average rate of change of f on an interval [a, b] is given by: Δy/Δx = Δy/Δt = [f(b) - f(a)] / (b - a) On a graph, the average rate of change is the slope of the secant line through the points (a, f(a)) and (b, f(b)). Example: Pompompurin wakes up in the morning and plans to eat pudding before he takes a nap in the evening. The number of pudding cups he eats is given by y = f(t) = t² - t, where t is measured in hours. a) Find the average rate of change of f on the interval. Then explain your answer in the context of the problem. Try to work through it yourself first! Δy/Δt = [f(2) - f(1)] / (2 - 1) = [(2² - 2) - (1² - 1)] / 1 = (2 - 0) / 1 = 2 This means that between 1 and 2 hours, Pompompurin is eating at an average rate of 2 pudding cups per hour. b) Graph the number of pudding cups Pompompurin is eating from t = 0 to t = 8 and interpret your graph in the context of the problem. At t = 0, or when Pompompurin first wakes up, he has eaten 0 pudding cups. Δy/Δt = [f(8) - f(0)] / (8 - 0) = [(8² - 8) - (0² - 0)] / 8 = (56 - 0) / 8 = 7 This means that between 0 and 8 hours, Pompompurin is eating at an average rate of 7 pudding cups per hour. That's a lot of pudding!#math #sanrio #fyp #pompompurin #calculus](/video/cover/7686304265635138846.webp)
