Question

Ibuprofen treats inflammation and is also an everyday painkiller for a range of aches and pains. Its half-life in the bloodstream is 1.8 hours. If you have a toothache and take a dose of ibuprofen at 12 noon, what percentage of the original dose of ibuprofen would still be in your

bloodstream at 6 p.m. on the same day? Round your answer to the nearest tenth of a percent.
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Answer 1

The half-life of ibuprofen in the bloodstream is 1.8 hours, which means that every 1.8 hours, the amount of ibuprofen in the bloodstream is reduced by half. We can use this information to calculate the percentage of the original dose of ibuprofen that would still be in your bloodstream at 6 p.m. if you took a dose at 12 noon.

There are 6 hours between 12 noon and 6 p.m., which is 3.33 half-lives (6 hours / 1.8 hours per half-life). This means that the amount of ibuprofen in the bloodstream would be reduced by half 3.33 times.

The percentage of the original dose of ibuprofen that would still be in your bloodstream at 6 p.m. is calculated as follows:

Percentage remaining = (1/2)^(number of half-lives) x 100%

Percentage remaining = (1/2)^(3.33) x 100%

Percentage remaining = 11.9%

Therefore, the percentage of the original dose of ibuprofen that would still be in your bloodstream at 6 p.m. on the same day is 11.9%.