If a drug has a half-life of 8 hours, approximately how much of the drug remains after 24 hours?
Understand the Problem
The question is asking us to calculate the remaining percentage of a drug after 24 hours given its half-life of 8 hours. We will determine how many half-lives fit into 24 hours and use that to find the remaining amount of the drug.
Answer
The remaining percentage of the drug after 24 hours is $12.5\%$.
Answer for screen readers
The remaining percentage of the drug after 24 hours is $12.5%$.
Steps to Solve
- Determine the number of half-lives in 24 hours
To find out how many half-lives fit in 24 hours, divide the total time (24 hours) by the length of one half-life (8 hours).
$$ \text{Number of half-lives} = \frac{24 \text{ hours}}{8 \text{ hours}} = 3 $$
- Use the half-life formula to find the remaining percentage
The percentage of the drug remaining after each half-life is given by the equation:
$$ \text{Remaining Percentage} = \left( \frac{1}{2} \right)^n \times 100 $$
where $n$ is the number of half-lives.
For our case:
$$ \text{Remaining Percentage} = \left( \frac{1}{2} \right)^3 \times 100 $$
- Calculate the remaining percentage
Now, calculate the value:
$$ \text{Remaining Percentage} = \frac{1}{2^3} \times 100 = \frac{1}{8} \times 100 = 12.5% $$
The remaining percentage of the drug after 24 hours is $12.5%$.
More Information
This calculation assumes a constant decay rate characteristic of first-order kinetics, common for many drugs. Understanding half-lives is crucial in pharmacology as it helps determine how frequently a drug should be administered.
Tips
- Forgetting to convert the number of half-lives into a decimal percentage when calculating the remaining drug amount.
- Miscalculating the half-life durations; make sure to check the numbers used in your division.
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