Final answer:
It takes approximately 3.74 days for the level of Warfarin sodium in the body to be reduced to 20% of the original level, based on its half-life of 38 hours and using the exponential decay formula.
Step-by-step explanation:
To calculate the time it takes for the drug level in the body to be reduced to 20% of the original level, given a half-life of 38 hours, we use the concept of half-lives from exponential decay. Since the half-life of Warfarin sodium is 38 hours, in one half-life, the amount of the drug in the body will be reduced to 50% of its initial amount. To reach 20%, we need to find how many half-lives it takes to go from 100% to 20%.
The formula for exponential decay is:
Q(t) = Q_0 * (0.5)^(t/T)
where:
Q(t) is the quantity remaining after time t,
Q_0 is the initial quantity,
T is the half-life period, and
t is the time elapsed.
We want Q(t)/Q_0 = 0.20 (20%), and we know T = 38 hours.
0.20 = (0.5)^(t/38)
To find t, we take the natural logarithm of both sides:
ln(0.20) = (t/38)ln(0.5)
t = (ln(0.20) / ln(0.5)) * 38
Calculating this, we find:
t ≈ 89.70 hours
Since there are 24 hours in a day, we divide this number by 24 to get the number of days:
t ≈ 89.70 / 24 ≈ 3.74 days
Therefore, it takes approximately 3.74 days for the drug level to reduce to 20% of the original level in the body.