SOLUTION: Hello I have a huge homework problem. Any help will be most appreciated, as I am bad at word problems. Here goes Patients with acute serious infections such as Salmonella Typhi or

Question 538837: Hello I have a huge homework problem. Any help will be most appreciated, as I am bad at word problems. Here goes
Patients with acute serious infections such as Salmonella Typhi or gram negative bacteria causing meningitis can be treated with regular doses of Chloramphenicol. A patient weighing 150 pounds requires a dose of 850 milligrams, while a patient weighing 300 pounds requires a dose of 1700 milligrams.
Lab experiments indicated that the concentration level C in milligrams per milliliter of the medication in the above patient�s bloodstream is a function of the amount of time t, in hours, since the medication is given by the quadratic equation: C (t)=83.3t^2 + 583.1t-170.4. For a drug to have a beneficial effect, its concentration in the bloodstream must exceed a certain value, called the minimum therapeutic level. The minimum therapeutic level of Chloramphenicol is 125 mg/ml.Patient Weight: 240 lbs
The doctor wishes to use a 10% solution of Chloramphenicol, administered through an intravenous injection. The hospital only carries 5% and 20% solutions of the required medication.
1. Determine a linear function for determining the dosage needed for a patient based on the patients� weight in pounds.
2. Interpret the slope of this linear function
3. Determine the amounts of each type of solution required to prepare 1000 ml of the 10% solution

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
"A patient weighing 150 pounds requires a dose of 850 milligrams, while a patient weighing 300 pounds requires a dose of 1700 milligrams."
They seem to be hinting that the dose needed varies directly with the weight of the patient, and that we can calculate the dose by using the factor
about 5.67 mg/lb or 12.5 mg/kg.
The linear function they want in 1) is the line we would get from the two points given (the 150 pound patient and the 300 pound patient):

NOTE
Math nerds like me do not know that the relationship would be lineal, but I trained/worked in pharmacology and know that doses are often expressed per kilogram body weight (even when working with 20-gram mice), so direct relations are assumed.
2) The slope is the dose per pound ratio that you would use. You would multiply patient weight times that slope.
EXTRA INSIGHTS
Nowadays scales in hospitals give weight in kilograms and the nurse translates the reading into pounds for the patient's benefit (not that it will necessarily make the patient happy). Since the problem refers to pounds, this is an old problem or not a realistic one.
A 240 pound patient would need 1360 mg chloramphenicol , but you did not ask that question.
The equation does not make sense. It would mean that the patient's blood level would start negative (OK, maybe it's only a good model after half an hour or so), and would continue to increase forevermore.
If the blood levels would vary as they would be 125 mg/mL when , and

That would give you t=0.55 hours and t=6.45 hours.
I would give a dose every 6 hours, but you don't ask about that either.
3)"The doctor wishes to use a 10% solution of Chloramphenicol, administered through an intravenous injection. The hospital only carries 5% and 20% solutions of the required medication."
1000mL of a 10% solution would contain grams.
The amount in x mL of 5% solution would be grams.
The amount in (1000-x) mL of 20% solution would be grams.
So ---> ---> ---> ---> --->
You would use 667 mL of 5% solution and 333 mL of 20% solution.
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