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Math Help - decay rate of drug

  1. #1
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    Question decay rate of drug

    This problem is long, no idea how to start this..plz help
    Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anestheized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbital is eliminated exponentially from the dog's bloodstream, with a half-life of 5 h. what single dose should be adminstered in order to anesthetize a 50-kg dog for 1 h?
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  2. #2
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    Quote Originally Posted by DMDil View Post
    This problem is long, no idea how to start this..plz help
    Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anestheized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbital is eliminated exponentially from the dog's bloodstream, with a half-life of 5 h. what single dose should be adminstered in order to anesthetize a 50-kg dog for 1 h?
    Substitute x = \frac{1}{2} x_0 and t = 5 into x = x_0 e^{kt} and solve for k. So:

    x = x_0 e^{\left(-\frac{\ln 2}{5}\right) t}.

    Substitute x = (45)(50) and t = 1 and solve for x_0.
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