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A patient takes a 250mg does of medicine. Tests later show 40 mg of the half-life is 1.25 hours, how many hours ago was the medication taken? Round to the nearest tenth.

User Ordo
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1 Answer

3 votes

Answer:

  • 3.3 hours

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Use half-life formula:


  • N(t) = N_0(1/2)^(t/h),

where

  • N(t) - remaining quantity,
  • N₀ - initial quantity,
  • t - time elapsed,
  • h - half life of the substance

Substitute given values and solve for t:


  • 40 = 250(1/2)^(t/1.25)

  • 4/25 = (1/2)^(t/1.25)

  • ln\ (4/25)=(t/1.25)\ ln\ (1/2)

  • t=1.25\ ln\ (4/25)/ln\ (1/2)

  • t=3.3\ rounded
User Sameera Jayasoma
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