A steroid with a first order half-life of 42 days is taken once. How long until only one sixty-fourth of the dose remains?

1. Each half-life leaves half of whatever was there at its start. 2. After n half-lives the fraction remaining is one half raised to the power n. 3. One sixty-fourth is one half raised to the power 6, since 2 to the power 6 is 64. 4. So six half-lives must pass. 5. Six times 42 days is 252 days. 6. The answer 126 days is only three half-lives, which would leave one eighth. 7. The answer 210 days is five half-lives, which would leave one thirty-second. _Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.4 Integrated Rate Laws_