alexishonaker9105 alexishonaker9105
  • 02-12-2019
  • Mathematics
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The half life of a certain tranquilizer in the bloodstream is 37 hours. How long will it take for the drug to decay to 86% of the original decay model,A=A

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sqdancefan
sqdancefan sqdancefan
  • 02-12-2019

Answer:

  8.1 hours

Step-by-step explanation:

A model of the fraction remaining can be ...

  f = (1/2)^(t/37) . . . . t in hours

So, for the fraction remaining being 86%, we can solve for t using ...

  0.86 = 0.5^(t/37)

  log(0.86) = (t/37)log(0.5)

  t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours

It takes about 8.1 hours to decay to 86% of the original concentration.

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