Suppose Ct is the concentration of a drug in the bloodstream t hours after the initial...

Suppose C_t is the concentration of a drug in the bloodstream t hours after the initial dose is administered. Suppose the initial dose C₂was 217.6 ug/mL and suppose that every hour is administered 174 g/mL. If the body metabolizes and eliminates 54% of the concentration of the drug C_t over a period of one hour; determine C₂, the concentration of the drug in the bloodstream two hours after the initial dose is administered.

Response at two decimal valors.

Expert Solution

Suppose is the concentration of a drug in the bloodstream t hours after the initial dose is administered.

The initial dose was 217.6 micrograms per ml, so

The body metabolizes and eliminates 54% of the concentration of the drug in an hour, so, by just before completion of one hour, the body has metabolized

Therefore, at the 1 hour mark, the body had left micrograms per ml. Now, in the next hour, 174 micrograms per ml were administered once again, so after 1 hour the concentration of the drug in the body is

Again, over the next hour, the body uses up 54% of this, so

and again, 174 micrograms of the drug is administered, so, two hours after the initial dose is administered, the concentration of the drug in the blood is

which is the required answer. (300.08, rounded to two decimal places)

Colby Messinger answered 1 year ago

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