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,
= 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
Problem 7- Calculate
the value of the constant r.
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