A certain drug has a half-life of 2 hours in the bloodstream. The label says to take the drug every six hours. About how much of the drug will be in the bloodstream a month after the patient begins taking 700 mg every six hours?
in three halflives, you should have 1/8 left.
amountremaing=original*(1/2)^3 or
amount remaining= original*e^-.693*6/2
To find out how much of the drug will be in the bloodstream a month after the patient begins taking it, we need to calculate the number of doses taken over that period and determine the remaining amount of the drug after each dose.
First, let's find out the number of doses taken in a month. Since the label states to take the drug every six hours, we can derive the number of doses taken in a day by dividing 24 hours (number of hours in a day) by 6 hours:
Number of doses per day = 24 hours / 6 hours = 4 doses per day
Next, let's determine the number of days in a month. Since we need to calculate the drug amount after a month, we'll assume there are 30 days in a month.
Now, let's find the remaining amount of the drug after each dose is taken. The half-life of the drug is given as 2 hours, which means that every 2 hours, the amount of drug in the bloodstream reduces by half.
To start, the patient takes a dose of 700 mg. After 2 hours, the drug amount decreases to half of its initial value, which is 700 mg / 2 = 350 mg.
The patient takes another dose after 6 hours, so we start with the remaining amount from the previous calculation, which was 350 mg. After another 2 hours, the drug amount decreases to half, which is 350 mg / 2 = 175 mg.
This process is repeated after each dose, so we continue to divide the remaining drug amount by 2 every 2 hours until the month ends. Since each day has 4 doses, after 24 hours (4 doses x 6 hours), the drug amount will decrease by half 24/2 = 12 times.
So, the amount of drug remaining after one day is: 175 mg / 2^12 = 175 mg / 4096 = 0.04272 mg.
To find the amount of drug remaining after a month, which is 30 days, we multiply the remaining amount after one day by the number of days:
Drug remaining after a month = 0.04272 mg x 30 = 1.2816 mg.
Therefore, approximately 1.2816 mg of the drug will be in the bloodstream a month after the patient begins taking 700 mg every six hours.