A dosage of 50 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) 83 mL
B) 125 mL
C) 111 mL
D) 152 mL

Question

A dosage of 50 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) 83 mL 
B) 125 mL 
C) 111 mL 
D) 152 mL

Quizplus · Accepted Answer

We can use the formula for exponential decay to solve this problem. Let A be the initial dosage of 50 mL and r be the decay rate of 0.6. Then the amount of drug in the bloodstream after n doses is given by:

A_n = A * (1 - r)^n

We are given that A_11 = 25 mL. Solving for n, we get:

25 = 50 * (1 - 0.6)^n
0.5 = 0.4^n
log(0.5) = n * log(0.4)
n = log(0.5) / log(0.4)
n ≈ 2.32

So the eventual level of the drug is:

A_∞ = A * (1 - r)^∞
= 50 * (1 - 0.6)^∞
= 50 * 0
= 0 mL

Therefore, the best choice is C) 111 mL, rounded to the nearest mL.

A Dosage of 50 ML of a Drug Is Given