Question 1036616: What do the roots of this equation represent? How often should the patient take his/her medicines.
Suppose the equation  models the number of milligrams of a certain medication in the bloodstream t hours after it has been taken.
The doctor can use the roots of this equation to figure out how often the patient should take the medicine to keep a certain concentration in his/her body.
ty :)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Purely mathematically speaking, the function has 4 roots considering all real numbers as the domain. But this is not purely a mathematical statement -- it is a model of a real-life situation. Given that, we need to restrict the domain of the function to those values that make sense in the real world.
In the first place, any value of  that is less than zero can be ignored because the model is certainly invalid for any time before the medicine is taken. One of the zeros of the function is  so we can ignore that value.
The other three zeros,  ,  , and  appear on the figure below:
 .
Considering the red part of the graph we can see that there is zero medicine in the bloodstream at time 0, which makes sense (to me anyway). Then as time passes, the amount increases to a maximum of about 336 mg just after 2 hours has elapsed and then starts to decrease, becoming zero at 5 hours.
Anything after 5 hours, the model begins to no longer make sense. According to the function, after 5 hours, the patient's bloodstream is manufacturing the medicine and putting it back into the medicine bottle. An absurd idea, indeed.
So, even though the domain of the polynomial function is, like every other polynomial function, all real numbers, the practical domain of the real-world model is the interval  and the two roots of the function that are contained in this domain are the two points in time when the bloodstream contains zero milligrams of the medicine assuming a single dose given in a 5-hour period.
John
My calculator said it, I believe it, that settles it
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