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gabie1121

  • 2 years ago

When a patient is given a certain quantity Q0 of medication, in grams, the liver and kidneys eliminate about 40% of the drug from the bloodstream each hour, so that only 60% of the drug will remain in the system after each hour. We let Q(t) be the quantity of drug available in the body at any time t, in hours. (a) If Q0 = 250 mg, find Q(1), Q(2), and Q(3). (b) Find a formula for Q(t) as an exponential function of t, for t ≥ 0. (c) At what time t does 75 mg of the drug remain?

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  1. gabie1121
    • 2 years ago
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    I don't even have a clue as how to start or even what to google or look-up in my book for help

  2. gabie1121
    • 2 years ago
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    I got the answer for A, that was pretty straight forward

  3. gabie1121
    • 2 years ago
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    I have Q(1)=150, Q(2)=90, Q(3)=54

  4. zepdrix
    • 2 years ago
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    Hmm yah those looks correct. Part B) now huh? Hmmmm.

  5. gabie1121
    • 2 years ago
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    would it be like Q(t)=250-.6^t?

  6. gabie1121
    • 2 years ago
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    nope that doesnt work if i plug numbers in.. just a thought

  7. gabie1121
    • 2 years ago
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    oh its just 250*.6^t

  8. zepdrix
    • 2 years ago
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    Yay good job! C:

  9. gabie1121
    • 2 years ago
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    I figured that out by trail an error. I guess thats the way to do it! Lol thanks for the back up again

  10. gabie1121
    • 2 years ago
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    thanks! gave you a medal back

  11. zepdrix
    • 2 years ago
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    Able to figure out part C ok? :)

  12. gabie1121
    • 2 years ago
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    set it equal to 54 and solve for t, right?

  13. gabie1121
    • 2 years ago
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    i meant 75

  14. zepdrix
    • 2 years ago
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    Yah c: cool.

  15. gabie1121
    • 2 years ago
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    how would i get the t out of the exponent? I know to just divide by 250 on both sides

  16. zepdrix
    • 2 years ago
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    We have to use that nasty logarithm function to get it out of the exponent position! :O

  17. gabie1121
    • 2 years ago
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    then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]

  18. gabie1121
    • 2 years ago
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    ohh ew. hows that go again?

  19. zepdrix
    • 2 years ago
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    \[\large .3=.6^t\]If we take the natural log of both sides,\[\large \ln .3=\ln\left(.6^t\right)\]

  20. zepdrix
    • 2 years ago
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    Then we need to remember a handy rule of logs,\[\huge \log(a^{\color{orangered}{b}})=\color{orangered}{b} \log(a)\]

  21. gabie1121
    • 2 years ago
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    so ln.3=tln.6?

  22. gabie1121
    • 2 years ago
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    then just plug the two logs into my calculator and then divide over to solve for t?

  23. zepdrix
    • 2 years ago
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    Yep looks good \c:/ Mr Calculator has to finish it up for us!

  24. gabie1121
    • 2 years ago
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    awesome. thanks as always!

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