PRINTER VERSION ‘BACK The quantity of a drug, mg. present in the body t hours af

Question

PRINTER VERSION ‘BACK The quantity of a drug, mg. present in the body t hours after an injection of the drug is given bs 0-f(t) = 100t e-06t Find (1), (1)6), and (6). Give units and interpret the a Give units and interpret the answers Round your answers to two decimal places. Interpretation of f(1) and f (1) One hour after the drug was administered, the quantity of drug in the body is approximately B (1) mg and the quantity is decreasing at a rate of" (1,1 mg per hour Interpretation of (6) and f (6): Six hours after the drug the quantity of drug in the body is approximately was a

Explanation / Answer

Q=f(t)=100te-0.6t

f '(t)=(100*1*e-0.6t)+(100te-0.6t*(-0.6*1))

f '(t)=(100e-0.6t)+(100(-0.6t)e-0.6t)

f '(t)=100e-0.6t(1-0.6t)

f(1)=100*1*e-0.6*1 = 54.88 mg

f '(1)=100e-0.6*1(1- 0.6*1) =21.95 mg per hour

f(6)=100*6*e-0.6*6 =16.39 mg

f '(6)=100e-0.6*6(1- 0.6*6) =-7.10 mg per hour

f(1) and f '(1)

f(1)  mg and the quantity is increasing at a rate of |f '(1)| mg per hour

54.88 mg and the quantity is increasing at a rate of 21.95 mg per hour

f(6) and f '(6)

f(6)  mg and the quantity is decreasing at a rate of |f '(6)| mg per hour

16.39 mg and the quantity is decreasing at a rate of 7.10 mg per hour

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