Question

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?

Answer 1

I don't even have a clue as how to start or even what to google or look-up in my book for help

Answer 2

I got the answer for A, that was pretty straight forward

Answer 3

I have Q(1)=150, Q(2)=90, Q(3)=54

Answer 4

Hmm yah those looks correct. Part B) now huh? Hmmmm.

Answer 5

would it be like Q(t)=250-.6^t?

Answer 6

nope that doesnt work if i plug numbers in.. just a thought

Answer 7

oh its just 250*.6^t

Answer 8

Yay good job! C:

Answer 9

I figured that out by trail an error. I guess thats the way to do it! Lol thanks for the back up again

Answer 10

thanks! gave you a medal back

Answer 11

Able to figure out part C ok? :)

Answer 12

set it equal to 54 and solve for t, right?

Answer 13

i meant 75

Answer 14

Yah c: cool.

Answer 15

how would i get the t out of the exponent? I know to just divide by 250 on both sides

Answer 16

We have to use that nasty logarithm function to get it out of the exponent position! :O

Answer 17

then i'm left with \[\frac{ 75 }{ 250 }=.6^{t}\]

Answer 18

ohh ew. hows that go again?

Answer 19

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

Answer 20

Then we need to remember a handy rule of logs,\[\huge \log(a^{\color{orangered}{b}})=\color{orangered}{b} \log(a)\]

Answer 21

so ln.3=tln.6?

Answer 22

then just plug the two logs into my calculator and then divide over to solve for t?

Answer 23

Yep looks good \c:/
Mr Calculator has to finish it up for us!

Answer 24

awesome. thanks as always!