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College Algebra

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When a person has a cavity filled, the dentist typically administers a local anesthetic. After leaving the dentist's office, one's mouth often feels numb for several hours. If a shot of anesthesia is injected into the bloodstream at the time of the procedure (t=0), and the amount of anesthesia still in the bloodstream t hours after the initial injection is given by A=A0e^-0.5t, in how many hours will only 10% of the original anesthetic still be in the bloodstream?

  • College Algebra -

    we are solving

    .1 = 1(e^(-.5t)
    take ln of both sides
    ln .1 = ln (e^(-.5t))
    ln .1 = -.5t (1)
    t = ln .1/-.5 = 4.61 hrs
    = appr. 4 hours and 36 minutes

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