Average Vitamin C Amount Problem: Calvin takes a 200-mg vitamin C tablet at 8:00 a.m

Chapter 10, Problem 18

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Average Vitamin C Amount Problem: Calvin takes a 200-mg vitamin C tablet at 8:00 a.m. and another at 11:00 a.m. The quantity, y, in milligrams, of vitamin C remaining in his body after time x, in hours after 8:00 a.m., is given by the piecewise function shown in Figure 10-3h. a. Between 8:00 and 11:00, y = 200e0.3x. How much vitamin C remains in Calvins body at 11:00 a.m., before he takes the second pill? What was the average number of milligrams over that 3-h period? Figure 10-3hb. At 11:00 a.m., when Calvin takes the next200 mg of vitamin C, the value of y jumpsimmediately to 200 + k, where k is theamount of the first dose remaining at 11:00.Between 11:00 a.m. and 2:00 p.m., y = (200 + k)e0.3(x3). Find the averagenumber of milligrams over the 6-h periodfrom 8:00 a.m. to 2:00 p.m.c. The mean value theorem for integrals doesnot apply to y on the interval [0, 6] becausethe function is discontinuous at x = 3. Is theconclusion of the theorem true in spite ofthe discontinuity? Give numbers to supportyour conclusion.