A party store ordered 50 cases of balloons. The number of cases in stock t months after the order arrives is given by the equation 50e^(-.9t). What is the average number (exact and approximate) of cases in stock over the same 6 months?
What a strange store. The fewer balloons in stock, the more slowly people buy them.
Anyway, Integrate f(t) over [0,6]
F(t) = Int(50e^(-.9t)) = -55.55e^(-.9t)
F(6) - F(0) = -55.55e^-5.4 + 55.55 = 55.3
Divide that by the interval length to get the average value: 55.3/6 = 9.2