SOLUTION: Help with this half-life / log problem ? keeping in mind the equation C(t) = Co e ^ (r x t) it reads The average half-life elimination of Ambien would be calculated at app

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Help with this half-life / log problem ? keeping in mind the equation C(t) = Co e ^ (r x t) it reads The average half-life elimination of Ambien would be calculated at app      Log On


   



Question 900913: Help with this half-life / log problem ?

keeping in mind the equation C(t) = Co e ^ (r x t)
it reads
The average half-life elimination of Ambien would be calculated at approximately 12.5 hours. If someone is given a standard dose of Ambien of 10mg/L, find a model that describes the concentration of the Ambien drug in the bloodstream. Round your answer to the nearest thousandth
My teacher helped me set up the equation
5 = 10e ^ (-r x 12.5)
you rearrange it
C = 10e ^ - ( r x t )
My question is, how do you find r and do the model they are asking for?
thank you

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your general model in better notation is highlight_green%28C%28t%29=C%5Bo%5De%5E%28rt%29%29.
You will want to know the value for r, and you use the half-life fact to find r.
First, solve symbolically for r , and second, use C%28t%29=%281%2F2%29C%5Bo%5D with half-life time.

ln%28C%28t%29%29=ln%28C%5Bo%5D%29%2Bln%28e%5E%28rt%29%29
rt%2A1%2Bln%28C%5Bo%5D%29=ln%28C%28t%29%29
rt=ln%28C%28t%29%29-ln%28C%5Bo%5D%29
highlight%28r=%281%2Ft%29ln%28C%28t%29%2FC%5Bo%5D%29%29

Substitute the values for half-life:
highlight%28r=%281%2F12.5%29ln%281%2F2%29%29, you would use relative values for the concentrations; knowing C%28t%29 is HALF of C%5Bo%5D
when the half-life time has passed.

The value for the decay constant, highlight%28r=-0.05545%29;
Notice that r is NEGATIVE.

The decay model for Ambien: highlight_green%28highlight%28C%28t%29=C%5Bo%5De%5E%28-0.05545%2At%29%29%29.
If your standard dose is 10 mg/L, then the model for decay can be specifically written
highlight%28highlight%28C%28t%29=10%2Ae%5E%28-.05545t%29%29%29.