Final answer:
The concentration of the drug decreases by a factor of 64 in 24 hours and by a factor of 512 in 36 hours.
Step-by-step explanation:
The half-life of a drug in the bloodstream is the time it takes for the concentration of the drug to decrease to half its initial value. In this case, the half-life is 4 hours. To calculate the factor by which the concentration decreases, we need to determine the number of half-lives that occur in a given time period.
In 24 hours, there are 6 half-lives (24 hours / 4 hours per half-life). Each half-life decreases the concentration by a factor of 2, so in 24 hours, the concentration decreases by a factor of 2⁶, which is 64.
In 36 hours, there are 9 half-lives (36 hours / 4 hours per half-life). Each half-life decreases the concentration by a factor of 2, so in 36 hours, the concentration decreases by a factor of 2⁹, which is 512. So therefore the concentration of the drug decreases by a factor of 64 in 24 hours and by a factor of 512 in 36 hours.