5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized
when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per
kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated
from the dog's bloodstream at a rate which is proportional to the amount of sodium
pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed
sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value
differential equation. What single dose should be administered in order to anesthetize a 50-kg
dog for 1 hr?
Transcribed Image Text:5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?
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