Question

A certain drug has a half-life in the body of 2.5 hours. What should the interval between doses be if the concentration of the drug in the body should not fall below 45% of its initial concentration? Round your answer to 2 significant digits.

Answer 1

To determine the interval between doses of a drug with a given half-life, calculate the number of half-life intervals needed for the concentration to reach the desired level, then multiply it by the half-life of the drug.

Step-by-step explanation:

The interval between doses of a certain drug should be determined based on its half-life and the desired concentration in the body. In this case, the half-life of the drug is 2.5 hours. To maintain a concentration not falling below 45% of the initial concentration, we need to calculate how many half-life intervals will be required for the concentration to reach 45%. Here are the steps:

1. Calculate the number of half-life intervals needed. Divide the natural logarithm of 45% (0.45) by the natural logarithm of 0.5 (since 50% is one half-life). This gives:
2. [Number of half-life intervals] = log(0.45) / log(0.5)
3. Calculate the time interval between doses. Multiply the number of half-life intervals by the half-life of the drug. This gives:
4. [Interval between doses] = [Number of half-life intervals] * [Half-life of the drug]
5. Round the answer to 2 significant digits.

By following these steps, you can determine the appropriate interval between doses based on the half-life of the drug and the desired concentration in the body.