A medicine is administered to a patient. The amount of medicine M, in milligrams, in 1 mL of the patient’s blood, t hours after the injection, is
M(t)=-1/3t^2+t where 0<t<3
a. Find the rate of change in the amount M, 2h after the injection.
b. What is the significance of the fact that your answer is negative?

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  1. -(1/3) t^2 + t
    -1/(3 t^2) + t

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  2. If the first then
    dM/dt = -(1/3)(2t) + 1

    = -2t/3 + 1
    if t = 2
    dM/dt = -4/3 + 3/3 = -1/3

    the medicine is disappearing, presumably because it is eating bad guys.

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