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# Analysis of adminstartion of drugs using differential eqns

A drug that has an half life of 20 hours inside the human body and is administered intravenously (I.V.) into a patient. The rate of change of the drug in the body is proportional to the amount present.

Write a differential equation explaining the rate of change of the quantity of the drug and determine the constant proportionality.

The patient receives the drug I.V. at a continuous rate of 4mg/min. Write a differential equation describing the rate of change of the amount of the drug and calculate the solution assuming there is none of the drug initially present in the patient.

It takes 2 hours for the I.V. bag to empty. How much of the drug is in the patient's blood stream at this point.

#### Solution Preview

See attachment for specifics but the differential equation in first instance is

dN/dt=-lamda*N

Where NI is the amount of drug in the body at any time t

Solve for lamda ...

#### Solution Summary

From a problem involving the administration of drugs in the body and known parameters a differential equation is developed that describes the absorbtion of the drug in the body over time. Based on the said drugs half life in the body the decay constant is determined. The rate of adminstartion of the drug is then given and based on this the modified differential equation describing new data is formulated and the amount of drug present in the body after 2 hours is determined .

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