Question

The concentration of a certain drug in the human body has a half-life of 39 minutes. What fraction of the drug will remain in the body 5 hours after consumption?

Answer 1

Explanation:

To find the fraction of the drug that remains in the body after 5 hours, you can use the concept of half-life.

The half-life of the drug is 39 minutes, which is equivalent to 39/60 hours (since there are 60 minutes in an hour).

Now, you want to calculate how many half-lives have passed in 5 hours:

Number of half-lives = (5 hours) / (39/60 hours per half-life) = (5 * 60) / 39 = 300 / 39

Now, find the fraction of the drug that remains:

Fraction remaining = (1/2)^(Number of half-lives)

Fraction remaining = (1/2)^(300/39)

You can leave it in this form or calculate the decimal approximation. Using a calculator:

Fraction remaining ≈ 0.00000572

So, approximately 0.00000572, or about 5.72 x 10^(-6), of the drug will remain in the body after 5 hours.