SOLUTION: Certain drugs are eliminated from the bloodstream at an exponential rate. Doctors and pharmacists need to know how long it takes for a drug to reach a certain level to determine ho

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Question 1003537: Certain drugs are eliminated from the bloodstream at an exponential rate. Doctors and pharmacists need to know how long it takes for a drug to reach a certain level to determine how often patients should take medications. Answer the following questions about this situation.
Write an exponential model for the following situation. The drug dosage is 500 mg. The drug is eliminated at a rate of 5.2% per hour. Use D = the amount of the drug in milligrams and t = time in hours.
How much of the drug is left after 6 hours? Round to the nearest milligram.
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The retention rate of the drug is 100-5.02=94.8% per hour.
highlight%28D=500%2A%280.948%29%5Et%29.

The question asks for D when t=6.

D=500%280.948%29%5E6
D=500%2A0.725855252786417664
You can only take three significant figures:
highlight%28363%2Amilligrams%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write an exponential model for the following situation.
The drug dosage is 500 mg.
The drug is eliminated at a rate of 5.2% per hour.
Note: 100%-5.2% = 0.0948
Use D = the amount of the drug in milligrams and t = time in hours.
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Equation:
D(t) = 500*(0.948)^t
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How much of the drug is left after 6 hours? Round to the nearest milligram.
D(6) = 500*0.948^6 = 362.93 ml
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Cheers,
Stan H.
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