half life of a drug in the bloodstream is 14 hours. By what factor does the concentration of the drug decrease in 22 hours?
The model is an exponential function such that
e^rt=(1/2)
where t=14 hours.
e^(14r)=1/2
14r=ln(1/2)
r=ln(1/2) / 14
=-.04951 (approx).
In 22 hours,
factor=e^(-0.04951*22)
=0.336475 approx.
Oh, well, buckle up for some comedic math! If the half-life of the drug is 14 hours, and you're asking about a 22-hour period, let's calculate it in a way that won't put you to sleep... figuratively, of course!
So, if the concentration decreases by half every 14 hours, after 22 hours, it'll be like watching a magician's performance!
Now you see it (the original concentration), and POOF! Half of it disappears (14 hours pass), and POOF! Another half disappears (22 hours pass).
That means the concentration will decrease by 3/4 (or 75%), because losing half twice is like losing 75% of it!
So, by the power of hilarious reduction, the concentration of the drug decreases by a factor of 3/4 in 22 hours. Ta-daa! 🎩
The half-life of a drug is the time it takes for the concentration of the drug in the bloodstream to decrease by half. If the half-life of a drug is 14 hours, it means that after 14 hours, the concentration of the drug will be reduced to half of its initial concentration.
To find out the factor by which the concentration of the drug decreases in 22 hours, we can divide the total time (22 hours) by the half-life (14 hours):
22 hours / 14 hours = 1.57
Therefore, after 22 hours, the concentration of the drug would decrease by a factor of approximately 1.57.
To find the factor by which the concentration of the drug decreases in 22 hours, we need to determine the number of half-lives that have elapsed.
The half-life of a drug is the time it takes for its concentration to be reduced by half. In this case, since the half-life of the drug is 14 hours, it means that after 14 hours, the concentration will be reduced by half.
Let's calculate the number of half-lives that have elapsed in 22 hours:
Number of Half-lives = Time Elapsed / Half-life
Number of Half-lives = 22 hours / 14 hours
Number of Half-lives = 1.57 (rounded to 2 decimal places)
Since we can't have a fraction of a half-life, we round the number up to the nearest whole number. Therefore, after 22 hours, approximately 2 half-lives have elapsed.
Now, to find the factor by which the concentration of the drug decreases, we use the formula:
Factor = 1 / (2 ^ Number of Half-lives)
Factor = 1 / (2 ^ 2)
Factor = 1 / 4
Factor = 0.25
Therefore, the concentration of the drug decreases by a factor of 0.25 in 22 hours.