SOLUTION: Hello, Can someone please help me with this math problem it is from the textbook College Algebra. i)Problem: The level of a prescription drug in the human body over

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Question 149823This question is from textbook College Algebra
:
Hello,
Can someone please help me with this math problem it is from the textbook College Algebra.



i)Problem: The level of a prescription drug in the human body over time can be found using the formula:

L = D
_____________
1 - (1/2)^n/h

where D is the amount taken every n hours and H is the drug’s half-life in hours.
(1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours, then to what level does the drug build up over time?
(2) If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?
(3) What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours?

Thank you,
Droxygirl1001

 This question is from textbook College Algebra

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
L+=+D%2F%281-%280.5%29%5E%28n%2Fh%29%29
where D is the amount taken every n hours and H is the drug’s half-life in hours.
(1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours, then to what level does the drug build up over time?
L+=+D%2F%281-%280.5%29%5E%28n%2Fh%29%29
L+=+2.5mg%2F%281-%280.5%29%5E%2824%2F14%29%29
L+=+2.5mg%2F%281-%280.5%29%5E%281.714%29%29
L+=+2.5mg%2F%281-0.3048%29
L+=+2.5mg%2F%280.6952%29
L+=+3.59mg

(2) If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?
L+=+D%2F%281-%280.5%29%5E%28n%2Fh%29%29
5.58mg+=+2.5mg%2F%281-%280.5%29%5E%28n%2F14%29%29
%281-%280.5%29%5E%28n%2F14%29%29+=+2.5%2F5.58
-%280.5%29%5E%28n%2F14%29=+-0.552
log%28%280.5%29%5E%28n%2F14%29%29+=+log%280.552%29
%28n%2F14%29+%2A+log%280.5%29+=+-0.258
%28n%2F14%29+%2A+%28-0.301%29+=+-0.258
n%2F14+=+0.857
n+=+0.857%2A14
n+=+12
(3) What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours?
L+=+D%2F%281-%280.5%29%5E%28n%2Fh%29%29
L+=+2.5mg%2F%281-%280.5%29%5E%2812%2F14%29%29
L+=+5.58mg
L+=+D%2F%281-%280.5%29%5E%28n%2Fh%29%29
L+=+5%2F%281-%280.5%29%5E%2824%2F14%29%29
L+=5mg%2F%280.6952%29
L+=+7.19mg
Big difference