Ask Question
11 June, 23:48

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A (t) remaining in the body t hours later is given by A (t) = 10 (0.7) t and that in order for the drug to be effective, at least 4 milligrams must be in the body.

a. Determine when 2 milligrams is left in the body.

b. What is the half-life of the drug?

0
Answers (1)
  1. 12 June, 01:15
    0
    Answer: a - 4.512 hours

    b - 1.94 hours

    Step-by-step explanation:

    Given,

    a) A (t) = 10 (0.7) ^t

    To determine when 2mg is left in the body

    We would have,

    A (t) = 2, therefore

    2 = 10 (0.7) ^t

    0.7^t = 2:10

    0.7^t = 0.2

    Take the log of both sides,

    Log (0.7) ^t = log 0.2

    t log 0.7 = log 0.2

    t = log 0.2 / 0.7

    t = 4.512 hours

    Thus it will take 4.512 hours for 2mg to be left in the body.

    b) Half life

    Let A (t) = 1/2 A (0)

    Thus,

    1/2 A (0) = A (0) 0.7^t

    Divide both sides by A (0)

    1/2 = 0.7^t

    0.7^t = 0.5

    Take log of both sides

    Log 0.7^t = log 0.5

    t log 0.7 = log 0.5

    t = log 0.5/log 0.7

    t = 1.94 hours

    Therefore, the half life of the drug is 1.94 hours
Know the Answer?