Question 923988: Please help me to solve this word problem: Before the series of x rays are taken, a patient is injected with a special contrast mixture that highlights obstructions in his blood vessels. The amount of the original dose of contrast material remaining in the patient's bloodstream h hours after it is injected is given by h -3/2. How much of the contrast material remains in the patient's bloodstream 4 hours after the injection?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! There is a typo.
Your formula does not make sense.
With  , at  (administration time), and  hour,
you would have, respectively,
 and  as a result.
Those are negative numbers, and that does not make sense.
What's worse, at  hours, and at  hours ,
the formula would tell you that the amount in the bloodstream would be
 and  respectively.
It makes absolutely no sense to have negative levels in the blood at first, and then have the levels increase {linearly no less) with time.
The fraction of the original dose of contrast material remaining in the patient's bloodstream h hours after it is injected
must be something such as  , or  .
In general, that fraction of the initial dose should be  with some positive constants  and  .
It has to be that what remains is a fraction of what was administered,
starting as 1 (the whole amount administered) at hours after administration,
and decreasing exponentially with time.
You need the right formula to know what fraction (something like 1/5 or 20%) remains in the bloodstream.
If they want an amount in milligram of drug, you also need the dose administered.
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