A drug is injected into the bloodstream of a patient. The concentration of the d

Question

A drug is injected into the bloodstream of a patient. The concentration of the drug in the bloodstream (in milligrams per cubic centimeter) hours after the injection is given by Find the instantaneous rate of change of the drug concentration with respect to time at the following times:
(A)
(B) A drug is injected into the bloodstream of a patient. The concentration of the drug in the bloodstream (in milligrams per cubic centimeter) t hours after the injection is given by C(t) = 0.1t/t2 + 2 C'(.5) C'(3)Find the instantaneous rate of change of the drug concentration with respect to time at the following times:

Explanation / Answer

The instantaneous rate of change of drug concentration is given by derivative of the function C(t).

C'(t) = [(t^2+2)*0.1 - (0.1*t)*(2*t)] / (t^2+2)^2

C'(t) = (0.2 - 0.1*t^2)/ (t^2+2)^2

Therefore,

A. C'(0.5) = 0.0345 milligrams per cubic centimeter

and

B. C'(3) = -0.00578 milligrams per cubic centimeter

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