Drug Diffusion in the blood stream. After a drug is taken orally, the amount of

Question

Drug Diffusion in the blood stream. After a drug is taken orally, the amount of the drug in the bloodstream after t hours is f(t) units.

A) Is the amount of the drug in the bloodstream increasing or decreasing at t = 5 hours?

B) Is the graph of f(t) concave up or concave down at t = 5 hours?

C) When is the level of the drug in the bloodstream decreasing the fastest?

D) At what time is the greatest level of drug in the bloodstream reached?

E) When is the level of the drug in the bloodstream decreasing at the rate of 3 units per hour?

Explanation / Answer

a)amount of the drug in the bloodstream decreasing at t = 5 hours ,since f '(t) <0 at t =5

b) f(t) concave up at t = 5 hours, since f "(t)>0 at t =5

c)level of the drug in the bloodstream decreasing the fastest when t = 4 hours since f "(t)=0 and f "(t) changes its sign from negative to positive at t =4

d) greatest level of drug in the bloodstream reached at t= 2 hours since f '(t)=0 and f '(t) changes its sign  from positive to negative at t =2

e)at t =2.7 hours  level of the drug in the bloodstream decreasing at the rate of 3 units per hour

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