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Question 874134: Need Serious help.
The following rational function describes concentration in blood of a certain medicine taken once depending on the time.
Find: A) The horizontal or oblique asymptote (if any).
B) The vertical asymptote if any.
C) Describe their possible meanings.
f(x)=3/x+4
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I believe you meant
f(x)=3/(x+4) , which is the same as  .
It would make sense to define the function only for  ,
with  being the time since the medicine was administered.
In that case, the domain is restricted,to non-negative values of ,
and the denominator is never zero, so
A) there are no vertical asymptotes, meaning
C) ther is no time, , when the blood level is undefined/infinite.
B) There is a horizontal asymptote, and it is  because as grows without bounds,  approaches zero.
C) That horizontal asymptote means that the blood level will decrease, getting closer and closer to zero as time goes by.
If, we look at , without specifying the domain,
then,
A) there is a vertical asymptote at  , when  , the denominator, is zero.
C) that means at time  (4 units of time before the drug was administered), the blood levels are undefined.
The horizontal asymptote and its meaning are as above.
On the other hand,
f(x)=3/x+4 , which is the same as  ,
and does not make sense in this situation, is undefined at  .
A) The vertical asymptote is .
C) That means that at time zero (when the drug was administered), the level was undefined or infinite.
An undefined level could be interpreted as not being able to draw blood and check the level at the precise time the drug was administered, but it would be better to state that the domain of the function is for  if the level could be measured and was first measured at 5 minutes.
B)There is a horizontal asymptote, and it is  because as grows without bounds,  approaches  .
C) that means that a long time after the drug was administered, the blood level is and stays at forever (not reasonable).
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