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

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SUMMARY

The half-life of morphine in the bloodstream is definitively established as 3 hours. Given an initial concentration of 0.4 mg, it takes approximately 9 hours for the morphine level to decrease to 0.01 mg. For Kool-Aid powder, starting with an unknown initial amount (x0), after 1 minute, 3 grams remain, and after 3 minutes, 1 gram remains. The initial amount of Kool-Aid powder can be calculated, and the remaining amount after 5 minutes can also be determined through mathematical modeling.

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ayahouyee
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(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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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. :)
 

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