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gabie1121

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?

  • one year ago
  • one year ago

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  1. gabie1121
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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

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

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

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

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

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

    • one year ago
  7. gabie1121
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    oh its just 250*.6^t

    • one year ago
  8. zepdrix
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    Yay good job! C:

    • one year ago
  9. gabie1121
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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

    • one year ago
  10. gabie1121
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    thanks! gave you a medal back

    • one year ago
  11. zepdrix
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    Able to figure out part C ok? :)

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

    • one year ago
  13. gabie1121
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    i meant 75

    • one year ago
  14. zepdrix
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    Yah c: cool.

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

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

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

    • one year ago
  18. gabie1121
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    ohh ew. hows that go again?

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

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

    • one year ago
  21. gabie1121
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    so ln.3=tln.6?

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

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

    • one year ago
  24. gabie1121
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    awesome. thanks as always!

    • one year ago
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