the half-life of a certain drug in the bloodstream is 4 hours. what fraction of the original drug dose remains in 24 hours?
well, 24 = 4*6, so the amount left will be
(1/2)^6 = 1/64
thanks
To determine the fraction of the original drug dose that remains in 24 hours, we need to calculate the number of half-lives that have occurred during this time period.
Given that the half-life of the drug is 4 hours, we can divide 24 hours by 4 hours to find the number of half-lives:
24 hours / 4 hours = 6 half-lives
Each half-life reduces the drug concentration by half. Therefore, the fraction of the original drug dose remaining after 6 half-lives is:
1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64
So, after 24 hours, 1/64 (approximately 0.0156) of the original drug dose remains in the bloodstream.
To determine the fraction of the original drug dose that remains in 24 hours, we need to understand the concept of a half-life. The half-life is the time it takes for half of the substance to decay or disappear. In this case, the half-life of the drug is given as 4 hours.
To calculate the fraction of the original drug dose that remains after a certain period, we divide the elapsed time by the half-life and then raise 0.5 (which represents half) to the power of that quotient.
In this scenario, the elapsed time is 24 hours, and the half-life is 4 hours.
Step-by-step calculation:
1. Divide the elapsed time by the half-life: 24 hours divided by 4 hours equals 6.
2. Raise 0.5 to the power of the quotient obtained in step 1: 0.5^6.
Calculating 0.5^6 gives us 0.015625.
Therefore, after 24 hours, approximately 0.015625 (or 1.5625%) of the original drug dose remains in the bloodstream.