anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I don't even have a clue as how to start or even what to google or look-up in my book for help
anonymous
  • anonymous
I got the answer for A, that was pretty straight forward
anonymous
  • anonymous
I have Q(1)=150, Q(2)=90, Q(3)=54

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zepdrix
  • zepdrix
Hmm yah those looks correct. Part B) now huh? Hmmmm.
anonymous
  • anonymous
would it be like Q(t)=250-.6^t?
anonymous
  • anonymous
nope that doesnt work if i plug numbers in.. just a thought
anonymous
  • anonymous
oh its just 250*.6^t
zepdrix
  • zepdrix
Yay good job! C:
anonymous
  • anonymous
I figured that out by trail an error. I guess thats the way to do it! Lol thanks for the back up again
anonymous
  • anonymous
thanks! gave you a medal back
zepdrix
  • zepdrix
Able to figure out part C ok? :)
anonymous
  • anonymous
set it equal to 54 and solve for t, right?
anonymous
  • anonymous
i meant 75
zepdrix
  • zepdrix
Yah c: cool.
anonymous
  • anonymous
how would i get the t out of the exponent? I know to just divide by 250 on both sides
zepdrix
  • zepdrix
We have to use that nasty logarithm function to get it out of the exponent position! :O
anonymous
  • anonymous
then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]
anonymous
  • anonymous
ohh ew. hows that go again?
zepdrix
  • zepdrix
\[\large .3=.6^t\]If we take the natural log of both sides,\[\large \ln .3=\ln\left(.6^t\right)\]
zepdrix
  • zepdrix
Then we need to remember a handy rule of logs,\[\huge \log(a^{\color{orangered}{b}})=\color{orangered}{b} \log(a)\]
anonymous
  • anonymous
so ln.3=tln.6?
anonymous
  • anonymous
then just plug the two logs into my calculator and then divide over to solve for t?
zepdrix
  • zepdrix
Yep looks good \c:/ Mr Calculator has to finish it up for us!
anonymous
  • anonymous
awesome. thanks as always!

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