Thread: Can someone help me with this question ?;(

3. Modeling the Concentration of a Drug in the Bloodstream
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A drug trial is studying the efficacy of a new drug for thalassemia, a genetic disorder in which a patient is unable to properly synthesize the hemoglobin molecule in the blood. In the trial, the rate at which the drug is metabolized by the body is studied. The data from the trial is then used to construct a model for the drug’s metabolism. The concentration of a drug, in parts per million, in a patient’s blood t hours after the drug is administered is given by the function

​ F(t)=-5t^5+3t^4-6t^3-2t^2+60t
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a) We would like to determine when the drug is completely eliminated from the bloodstream. Find this value of time, t. Explain why an exact solution to this problem is possible.
b) What is the mathematical domain of this function? What is the practical domain for this function?

c) Sketch the function on the mathematical domain and clearly show all your steps. As part of your graphing procedure, calculate some extra points to refine the accuracy of your graph. Clearly show which portion of your graph is in the practical domain of the problem. Explain the shape of the graph in the problem context and estimate when the drug attains maximum concentration.

Hey Holden1131.

It's a good idea to show us what you have tried for this question, but for a) I'll start with the hint that if the concentration is removed from the system then the concentration will be 0.

I was wondering could that formulae (F(t)=-5t^5+3t^4-6t^3-2t^2+60t) be simplified into F(t) = 50t^5 if so we can give t or time a value say 10 hours so
F(10) = 50(10^5)-->F(10) = 5000000 --> F=500000 in parts per million at 10 hours ????? I would like to try the problem but Im not sure if this would be something I would want to simplify.

Look at the graph of this function. It is only 0 at once place, t = 0. Basically this function says that the concentration in the blood stream is increasing as time is increasing, basically, there is something wrong with the function or question.