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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
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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gabie1121Best ResponseYou've already chosen the best response.1
I don't even have a clue as how to start or even what to google or lookup in my book for help
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
I got the answer for A, that was pretty straight forward
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
I have Q(1)=150, Q(2)=90, Q(3)=54
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm yah those looks correct. Part B) now huh? Hmmmm.
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
would it be like Q(t)=250.6^t?
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
nope that doesnt work if i plug numbers in.. just a thought
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
oh its just 250*.6^t
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
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

gabie1121Best ResponseYou've already chosen the best response.1
thanks! gave you a medal back
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Able to figure out part C ok? :)
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
set it equal to 54 and solve for t, right?
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
how would i get the t out of the exponent? I know to just divide by 250 on both sides
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
We have to use that nasty logarithm function to get it out of the exponent position! :O
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
ohh ew. hows that go again?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large .3=.6^t\]If we take the natural log of both sides,\[\large \ln .3=\ln\left(.6^t\right)\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Then we need to remember a handy rule of logs,\[\huge \log(a^{\color{orangered}{b}})=\color{orangered}{b} \log(a)\]
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
then just plug the two logs into my calculator and then divide over to solve for t?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yep looks good \c:/ Mr Calculator has to finish it up for us!
 one year ago

gabie1121Best ResponseYou've already chosen the best response.1
awesome. thanks as always!
 one year ago
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