document.write( "Question 539456: 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.
\n" ); document.write( "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.
\n" ); document.write( "Background-your patient
\n" ); document.write( "Weight: 240 lbs
\n" ); document.write( "Doctors orders:
\n" ); document.write( "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.
\n" ); document.write( "1. Determine a linear function for determining the dosage needed for a patient based on the patients’ weight in pounds.
\n" ); document.write( "2. Interpret the slope of this linear function
\n" ); document.write( "3. The dosage in milligrams, of Chloramphenicol needed for your patient
\n" ); document.write( " I did a ratio based on the information above and got X= 1360mgs
\n" ); document.write( "So for someone who weighs 240 lbs a dose of 1360mgs is needed.
\n" ); document.write( "4. Graph the function
\n" ); document.write( "6. Determine the amounts of each type of solution required to prepare 1000 ml of the 10% solution
\n" ); document.write( "7. Determine the dosage in milliliters rounded to 2 decimal places, of the 10% solution needed for your patient. Recall that medications are expressed as percent solution where the percent solution indicates how many grams of the active ingredient are dissolved in 100 milliliters of diluting elements (usually water or saline)
\n" ); document.write( "8. Determine how long after the IV injection it takes for the medication to start working
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #353440 by KMST(5328)\"\" \"About 
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I recently solved that problem as problem Linear_Algebra/538837
\n" ); document.write( "\"C+%28t%29=83.3t%5E2+%2B+583.1t-170.4\" does not make sense. It would start to have an effect in half an hour, but soon after that your patient may die of an overdose, as the blood levels keep increasing all the time. That curve has a minimum, and it happens at t<0. You expect blood levels to go through a maximum a few hours after dosing, and then decrease. For that you need a negative leading coefficient.
\n" ); document.write( "\"C+%28t%29=+-83.3t%5E2+%2B+583.1t-170.4\" makes a lot more sense, and that's what I used to explain the problem.\r
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