The concentration of the drug in the blood is eliminated

Question and Solution

The concentration of the drug in the blood is eliminated from the body. This concentration decreases proportional to the

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The concentration of the drug in the blood is eliminated from the body. This concentration decreases proportional to the concentration level at time t with t = 0 corresponding to the time of the first dose. This can be modeled with the differential equation where C is the concentration of the drug at timet. After the initial dose of the drug, the concentration is 1.5 mg/ml. Experiments have shown that after 4 hours the concentration is 0.75 mg/ml. (Of course this depends on a patients size but we are going with an average adult here). We are also making the assumption that since the drug is administered intravenously that the concentration immediately jumps. This assumption is not unreasonable since the amount of time that passes before it reaches the peak is very small compared to our decay time. It has been determined that the minimum therapeutic level for this drug is 0.45 mg/L and the maximum safe level is 2.15 mg/ml. Determine if the patient was only given one dose how long the drug would remain effective. Based on your findings, would you recommend dosing every 2 hours, every 4 hours, every 6 hours or every 8 hours? Explain your recommendation. After solving the differential equation you get . I am not sure what to plug into C to find the time for this question. I started by plugging in 1.5 but get a negative time. What am I doing wrong?

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