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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    E. Use the exponential decay formula

  2. anonymous
    • 5 years ago
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    Can you show me how to set it up?

  3. anonymous
    • 5 years ago
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    first write the formula for exponential decay: I'm going to use my own variables for convience F=Ae^(kt)

  4. anonymous
    • 5 years ago
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    F=amount you have A=amount you start with k=constant t=time elapsed

  5. anonymous
    • 5 years ago
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    what you have to do first is find k, so using 3 hours and 18% we find k

  6. anonymous
    • 5 years ago
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    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

  7. anonymous
    • 5 years ago
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    so you have .82=1e^(3k)

  8. anonymous
    • 5 years ago
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    solve for k

  9. anonymous
    • 5 years ago
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    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.

  10. anonymous
    • 5 years ago
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    and that give me 10.5?

  11. anonymous
    • 5 years ago
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    how do I solve for K? im sorry

  12. anonymous
    • 5 years ago
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    .82=1e^(3k) Ln(.82)=3k k=Ln(.82)/3

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