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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?
I don't even have a clue as how to start or even what to google or look-up in my book for help
I got the answer for A, that was pretty straight forward
I have Q(1)=150, Q(2)=90, Q(3)=54
Hmm yah those looks correct. Part B) now huh? Hmmmm.
would it be like Q(t)=250-.6^t?
nope that doesnt work if i plug numbers in.. just a thought
I figured that out by trail an error. I guess thats the way to do it! Lol thanks for the back up again
thanks! gave you a medal back
Able to figure out part C ok? :)
set it equal to 54 and solve for t, right?
how would i get the t out of the exponent? I know to just divide by 250 on both sides
We have to use that nasty logarithm function to get it out of the exponent position! :O
then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]
ohh ew. hows that go again?
\[\large .3=.6^t\]If we take the natural log of both sides,\[\large \ln .3=\ln\left(.6^t\right)\]
Then we need to remember a handy rule of logs,\[\huge \log(a^{\color{orangered}{b}})=\color{orangered}{b} \log(a)\]
then just plug the two logs into my calculator and then divide over to solve for t?
Yep looks good \c:/ Mr Calculator has to finish it up for us!
awesome. thanks as always!