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gabie1121
 3 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?
gabie1121
 3 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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gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1I don't even have a clue as how to start or even what to google or lookup in my book for help

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1I got the answer for A, that was pretty straight forward

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1I have Q(1)=150, Q(2)=90, Q(3)=54

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Hmm yah those looks correct. Part B) now huh? Hmmmm.

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1would it be like Q(t)=250.6^t?

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1nope that doesnt work if i plug numbers in.. just a thought

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1I figured that out by trail an error. I guess thats the way to do it! Lol thanks for the back up again

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1thanks! gave you a medal back

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.1Able to figure out part C ok? :)

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1set it equal to 54 and solve for t, right?

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1how would i get the t out of the exponent? I know to just divide by 250 on both sides

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

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1ohh ew. hows that go again?

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

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

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1then just plug the two logs into my calculator and then divide over to solve for t?

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

gabie1121
 3 years ago
Best ResponseYou've already chosen the best response.1awesome. thanks as always!
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