anonymous
  • anonymous
The amount of a drug in a person's bloodstream can be modeled with exponential decay. Suppose that, in 3 hours, 18% of the drug is removed from the bloodstream. What is the half-life of the drug? A) 8.1 hours B) 8.7 hours C) 9.3 hours D) 9.9 hours E) 10.5 hours
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
E. Use the exponential decay formula
anonymous
  • anonymous
Can you show me how to set it up?
anonymous
  • anonymous
first write the formula for exponential decay: I'm going to use my own variables for convience F=Ae^(kt)

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anonymous
  • anonymous
F=amount you have A=amount you start with k=constant t=time elapsed
anonymous
  • anonymous
what you have to do first is find k, so using 3 hours and 18% we find k
anonymous
  • anonymous
assume you start with 100% so A=1 F=1-.18=.82 <---- this is cause you remove .18 from the blood, leaving you with .82
anonymous
  • anonymous
so you have .82=1e^(3k)
anonymous
  • anonymous
solve for k
anonymous
  • anonymous
then plug k into the equation. this time F=.5 since you are left with half the amount and t is what you are trying to find.
anonymous
  • anonymous
and that give me 10.5?
anonymous
  • anonymous
how do I solve for K? im sorry
anonymous
  • anonymous
.82=1e^(3k) Ln(.82)=3k k=Ln(.82)/3

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