# Calculus

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