Find Half-Life of Morphine & Kool-Aid Powder in Blood/Water

In summary, the conversation discusses two problems involving related rates. The first problem involves finding the amount of time it takes for the concentration of morphine in the bloodstream to decrease from 0.4 mg to 0.01 mg, given a half-life of 3 hours. The second problem involves finding the initial amount of Kool-Aid powder in a glass of water and the amount remaining after 5 minutes, given that 3 grams remain after 1 minute and 1 gram remains after 3 minutes. The request for help is declined as the forum aims to guide, not solve, problems.
  • #1
ayahouyee
12
0
(a) The half-life of morphine in the bloodstream is 3 hours. Suppose that there's
initially 0.4 mg of morphine in the system, how long does it take until there's
only 0.01 mg of morphine remaining in the bloodstream?

(b) Suppose that there is initially x0 (0 is a subscript) grams of Kool-Aid powder in a glass of water.
After 1 minute there are 3 grams remaining and after 3 minutes there is only 1
gram remaining. Find x0 (0 is a subscript) and the amount of Kool-Aid powder remaining after 5 minutes.

Thanks in advance!
 
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  • #2
Re: related rates 3

Hi ayahouyee, (Wave)

Welcome to MHB!

We want to help you know how to do these problems on your own, so if we just do them for you that won't really be the best way to do this. We can work with you to solve your problems together.

So what have you tried? Show us where you first get stuck and we can help you keep going. :)
 

FAQ: Find Half-Life of Morphine & Kool-Aid Powder in Blood/Water

What is the half-life of morphine in the body?

The half-life of morphine in the body is approximately 2-4 hours. This means that after this amount of time, half of the initial amount of morphine in the body will have been metabolized and eliminated.

What factors can affect the half-life of morphine in the body?

The half-life of morphine can be affected by a number of factors including age, liver and kidney function, body mass, and the presence of other drugs in the body.

How is the half-life of morphine determined?

The half-life of morphine is determined through pharmacokinetic studies where blood samples are taken at specific time intervals after administration of the drug. The concentration of morphine in the blood is then measured and used to calculate the half-life.

What is the half-life of Kool-Aid powder in water?

The half-life of Kool-Aid powder in water is not applicable in the same way as drugs. Kool-Aid powder will dissolve completely in water and will not have a measurable half-life.

Can the half-life of morphine be accurately determined in blood or water samples?

Yes, the half-life of morphine can be accurately determined in blood or water samples through laboratory testing. However, it is important to note that the half-life may vary between individuals and may not be the same in different bodily fluids.

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