Level of prescrip. drug in human body formula...

[jlaw]

Hello E-Instructors

Would someone kindly show me how to solve this problem correctly?

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.
(''''These marks are merely spacers and not intended to be part of the equation).

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?

So far I think that the formula may look like this:
2.5 = ___24________
'''''''''''''''''1-(1/2)^24/14

Then maybe this:
2.5 = ___24____
''''''''''''''''''0.3047534

2.5 = 69.057991

Then, I don't know what to do next or if what I've done is even close to being right.

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?

I'm completely in the dark about this one.

3. What is the difference between taking 2.5 milligram of Lorazepam
every 12 hours and taking 5 milligrams every 24 hours?

This one, I might subtract results from these two equations:

2.5 = ___12_________
'''''''''''''''''1-(1/2)^12/14
from
5 = ___24_______
''''''''''1-(1/2)^24/14

Well, that would be after I have learned how to solve the first question
correctly.

Thank you so much for sharing your valuable knowledge with a mathematically challenged damsel like myself.
Grateful,
Julia

 

[tkhunny]

L= ___D___
''''''''1-(1/2)^n/H

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?

So far I think that the formula may look like this:
2.5 = ___24________
'''''''''''''''''1-(1/2)^24/14

Why did you substitute for L?

You are given:
D = 2.5 mg
n = 24 hr
H = 14 hr

Use these to calculate L

Where did you get D=24 in the numerator? I think you're guessing. Just substitute the given values.

 

[jlaw]

Thanks Tkhunny!

So, the formula would look like this?
L= ___2.5_____
'''''''''1-(1/2)^24/14

L = ____2.5_____
''''''''''' 0.3047534

L = 8.2 milligrams level build up over time?

This sight suggests inquirers attempt to solve the problem, because I'm still an infant to algebra, I could only take a blind poke in the dark (and ask a professional) at something that I do not yet understand.... you were right. I was guessing, in an attempt to show effort on my part. If you prefer, In the future I could just said "I don't know" and not totally flop on attempting a solution. I'm flexible, just let me know the protocol. :0)

 

[stapel]

This sight suggests inquirers attempt to solve the problem, because I'm still an infant to algebra, I could only take a blind poke in the dark...

So this material hasn't yet been covered in class...?

(You posted this to "Intermediate / Advanced Algebra", which means you've completed beginning algebra. Evaluation [plugging the given values into the given variables], which is all that was required here, is generally covered in pre-algebra....)

Eliz.

 

[tkhunny]

In the future I could just said "I don't know"...

Bad idea. That will just alarm me and I will tell you that you are in the wrong class and that you need to have a heart-to-heart with your academic advisor, or maybe that you cheated on your placement exam, or maybe that you have been sleeping in class. The concept of "No Idea" is very unsettling.

Here is a protocol...

1) WRITE DOWN what you are planning.
2) Don't do anything that totally fails to make sense.
3) Make sure you end up with what the question is asking. Check multiple times.

In this case, a clear and concise definition of the required substitutions would have helped. See my first post. If you WRITE DOWN "D = 2.5 mg", you are very unlikely to substitute this value for "L". That can't make sense and will violate protocol #2.