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4. (5pts) A patient is given a 30mg shot of medication every day at the same time. Immediately after
the shot, the patient’s blood is tested to see how much of the medication is in her bloodstream.
Experiment indicates that after 24 hours of the previous day’s observed amount of medicine remains
in the patient’s bloodstream. So, after the first shot the patient is fouhd to have 30mg of medication in
their bloodstream. The next day after the second shot, the patient is found to have 30mg of medication
in their bloodstream from the second shot, plus of the previous day’s amount; that makes 30+()(30)
mg. After the third shot, the patient will have 30 + ()(30 + ()(30)) = 30 + 30(f) + 30()2 mg. If
this continues indefinitely, how much medication will the patient eventually have in her bloodstream?
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