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Solve the Problem A0A _ { 0 } Of the Drug in the Bloodstream at the Time of Treats

question 29

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Solve the problem.
-The attending physician in an emergency room treats an unconscious patient suspected of a drug overdose. The physician does not know the initial concentration A0A _ { 0 } of the drug in the bloodstream at the time of injection. However, the physician knows that after 3hr3 \mathrm { hr } , the drug concentration in the blood is 0.75μg/dL0.75 \mu \mathrm { g } / \mathrm { dL } and after 4hr4 \mathrm { hr } , the concentration is 0.719μg/dL0.719 \mu \mathrm { g } / \mathrm { dL } . The model A(t) =A0ektA ( t ) = A _ { 0 } \mathrm { e } ^ { - k t } represents the drug concentration A(t) A ( t ) (in μg/dL) \mu \mathrm { g } / \mathrm { dL } ) in the bloodstream tt hours after injection. The value of kk is a constant related to the rate at which the drug is removed by the body.

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Definitions:

Base Year

A specific year against which economic or financial data is compared, often used to calculate indices or real growth rates.

Current Year

The ongoing year according to the Gregorian calendar, continuously updating as time progresses.

Paasche Price Index

A price index that measures the price changes between the current and base period by using the current period quantities as weights.

Doggerel

Doggerel denotes poorly written verse, often characterized by its triviality or nonsensical content.

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