Exponential functions can be used to model the concentration of a drug in a patient's body. Suppose the concentration of Drug X in a patient's bloodstream is modeled by,

C (t) = C₀ e ^{- rt},

where C (t) represents the concentration at time t (in hours), C₀ is the concentration of the drug in the blood immediately after injection, and r > 0 is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug (C₀ ) peaks immediately when the drug is injected.

 

Using this model, try to solve the following problems:

Problem 1-Find the concentration of drug in the blood at a given time after injection.

Problem 2- Calculate the value of r given data on the concentration of a drug in the blood over time.

Problem 3- Calculate the time it takes for the blood concentration of a drug to decrease by a given percentage.

Problem 4- Calculate the initial dose of a drug that needs to be administered.

Problem 5- Calculate when a second dose of a drug needs to be given.

Problem 6- Determine the time it takes for the blood concentration of a drug decrease by a given percentage.

Problem 7- Calculate the value of the constant r.

 

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