Drug Concentration If a drug is administered intravenously then the amount of drug in the bloodstream...

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Drug Concentration If a drug is administered intravenously then the amount of drug in the bloodstream starts at 0 and increases until the rate at which the drug enters the bloodstream (through the IV infusion) is equal to the rate at which it is leaving the bloodstream (through metabolization and elimination). It turns out that the amount of drug in the bloodstream t hours after an IV infusion begins is T B(t) = (1-ekt), where r is the rate of infusion in mg per hour, k is a constant that depends on the drug, and B(t) is measured in mg. If a drug is administered through rapid injection, then the amount of drug in the bloodstream starts out very high immediately after the injection, then decreases as the body eliminates it. If a drug is administered by a rapid injection, followed by an IV infusion, then the amount of drug in the bloodstream after t hours is D(t) = Dekt + (1 - ekt). where D is the initial injection dose. Suppose that for a certain drug k = -0.12. MATH 102 6. Suppose that this drug has been administered through rapid injection followed by IV infusion, with an initial injection of D = 80mg. If we know that D'(t) = 0.4e-0.12t how could we use antiderivatives to find the rate of infusion, r? Hint: You know that D(0) = 80, so use an antiderivative to find D(t) and then compare that with our model. Drug Concentration If a drug is administered intravenously then the amount of drug in the bloodstream starts at 0 and increases until the rate at which the drug enters the bloodstream (through the IV infusion) is equal to the rate at which it is leaving the bloodstream (through metabolization and elimination). It turns out that the amount of drug in the bloodstream t hours after an IV infusion begins is T B(t) = (1-ekt), where r is the rate of infusion in mg per hour, k is a constant that depends on the drug, and B(t) is measured in mg. If a drug is administered through rapid injection, then the amount of drug in the bloodstream starts out very high immediately after the injection, then decreases as the body eliminates it. If a drug is administered by a rapid injection, followed by an IV infusion, then the amount of drug in the bloodstream after t hours is D(t) = Dekt + (1 - ekt). where D is the initial injection dose. Suppose that for a certain drug k = -0.12. MATH 102 6. Suppose that this drug has been administered through rapid injection followed by IV infusion, with an initial injection of D = 80mg. If we know that D'(t) = 0.4e-0.12t how could we use antiderivatives to find the rate of infusion, r? Hint: You know that D(0) = 80, so use an antiderivative to find D(t) and then compare that with our model.

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