[SPLIT] elimination of Valium from bloodstream

[joyce.anderson]

The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours. Suppose that a patient receives an initial dose of 75 milligrams of valium at midnight.
a. How much valium is in the patient's blood at noon the next day?
b. Estimate when the Valium concentration will reach 35
% of its initial level.
Please step by step

 

[galactus]

Please start your own thread instead of posting in someone elses. Folks are better apt to see it that way.

Anyway, half life is given by the simple formula \(\displaystyle T=\frac{-1}{k}ln(2)\)(I will not bother with its derivation).

To find k, solve \(\displaystyle 36=\frac{-1}{k}ln(2)\) for k.

Then, sub that into \(\displaystyle y=75e^{kt}\) to find what you need.

for part a, plug in t=12.

for part b, find 35% of 75 and plug in for y, then solve for t.