## gabie1121 Group Title 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

1. gabie1121 Group Title

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

2. gabie1121 Group Title

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

3. gabie1121 Group Title

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

4. zepdrix Group Title

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

5. gabie1121 Group Title

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

6. gabie1121 Group Title

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

7. gabie1121 Group Title

oh its just 250*.6^t

8. zepdrix Group Title

Yay good job! C:

9. gabie1121 Group Title

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

10. gabie1121 Group Title

thanks! gave you a medal back

11. zepdrix Group Title

Able to figure out part C ok? :)

12. gabie1121 Group Title

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

13. gabie1121 Group Title

i meant 75

14. zepdrix Group Title

Yah c: cool.

15. gabie1121 Group Title

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

16. zepdrix Group Title

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

17. gabie1121 Group Title

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

18. gabie1121 Group Title

ohh ew. hows that go again?

19. zepdrix Group Title

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

20. zepdrix Group Title

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

21. gabie1121 Group Title

so ln.3=tln.6?

22. gabie1121 Group Title

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

23. zepdrix Group Title

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

24. gabie1121 Group Title

awesome. thanks as always!