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Consider a drug that is taken in 50 mg doses daily. Suppose that the first dose is taken when t=0 and that t is measured in hours. A.If the half-life of the drug is 6.4 hours, what fraction of the drug remains in the patient after 24 hours? fraction =

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Answer:

The remaining drugs will be [tex]\frac{1}{8} \sqrt[4]{\frac{1}{8} }[/tex] of the initial amount, or about 3.72 mg.

Step-by-step explanation:

To find the fraction of the drug remains in the patient after 24 hours, we can use the half life formula:

[tex]\boxed{N=\left(\frac{1}{2} \right)^{\frac{t}{T} }\cdot N_o}[/tex]

where:

  • N = total amount of remain particles
  • t = total amount of time
  • T = half-life time
  • N₀ = initial amount of particles

Given:

  • t = 24 hours
  • T = 6.4 hours
  • N₀ = 50 mg

[tex]\displaystyle N=\left(\frac{1}{2} \right)^{\frac{t}{T} }\cdot N_o[/tex]

   [tex]=\left(\frac{1}{2} \right)^{\frac{24}{6.4} }\cdot N_o[/tex]

   [tex]=\frac{1}{8} \sqrt[4]{\frac{1}{8} } \cdot N_o[/tex]

   [tex]=\frac{1}{8} \sqrt[4]{\frac{1}{8} } \cdot(50)[/tex]

   [tex]=6\frac{1}{4} \sqrt[4]{\frac{1}{8} } \ mg[/tex]

   [tex]\approx 3.72\ mg[/tex]

   

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