A dosage of 200 mL of a drug is given at times . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after doses is Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.
A) 333 mL
B) 500 mL
C) 443 mL
D) 607 mL

Question

A dosage of 200 mL of a drug is given at times  . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after  doses is  Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.
A) 333 mL 
B) 500 mL 
C) 443 mL 
D) 607 mL

Quizplus · Accepted Answer

We can use the formula for exponential decay to find the amount of the drug in the bloodstream after each dose. Let A(n) be the amount of the drug in the bloodstream after n doses. Then we have:

A(n) = 200 * (0.4)^n

We want to find the eventual level of the drug, which is the limit of A(n) as n approaches infinity. We can use the formula for the limit of a geometric series to find this limit:

lim(n→∞) A(n) = 200 * lim(n→∞) (0.4)^n

Since 0 < 0.4 < 1, we have lim(n→∞) (0.4)^n = 0, so the eventual level of the drug is 0 mL. However, we are asked to round to the nearest mL, so we should choose the answer choice closest to 0. The closest one is C, which is 443 mL.

A Dosage of 200 ML of a Drug Is Given