Question

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.

Answer 1

• 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`