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*)
= *C*_{0} *e*^{ - rt},

where *C* (*t*) represents
the concentration at time *t* (in hours), *C*_{0} 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 (*C*_{0} ) 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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