SOLUTION: The remaining concentration of a drug in a person’s bloodstream is modeled by the relation ​᠎​​᠎​C=C0(1/2)^t/8, where C is the remaining concentration of the drug in

Algebra ->  Exponents -> SOLUTION: The remaining concentration of a drug in a person’s bloodstream is modeled by the relation ​᠎​​᠎​C=C0(1/2)^t/8, where C is the remaining concentration of the drug in       Log On


   

Question 1196943: The remaining concentration of a drug in a person’s bloodstream is modeled by the relation ​᠎​​᠎​C=C0(1/2)^t/8, where C is the remaining concentration of the drug in the bloodstream in milligrams per milliliter of blood, C0 is the initial concentration, and t is the time, in hours, that the drug is in the bloodstream.
What is the half-life of this drug?
A nurse gave a patient this drug, which was 20 mg/ml. What is the concentration of this drug in 3.5 hours?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i think your equation is C = C0 * (1/2) ^ (t/8)
half life formula would be .5 = (1/2) ^ (t/8)
take the log of both sides of this equation to get:
log(.5) = log((1/2)^(t/8))
by log rules, this becomes:
log(.5) = t/8 * log(1/2)
solve for t/8 to get:
t/8 = log(.5) / log(.5) = 1
solve for t to get:
t = 8
half life of C is equal ti 8 hours.
confirm by replacing t with 8 to get:
C = (1/2) ^ (8/8) = (1/2) ^ 1 = (1/2)
if the initial dose was 20, then the formula becomes:
C = 20 * (1/2) ^ (3.5/8) = 14.76826146.
that should be your solution.
the equation can be graphed as shown below:

from the graph you can see that the initial concentration is 20 at x = 0 and the half life is 10 at x = 8 and the amount remaining at x = 3.5 is 14.768.
x is the number of hours.
y is the amount of drug remaining in the system.