Final answer:
The drug would take approximately 120 hours (or 5 days) to be eliminated, or have less than 10% of the dose remaining, given its half-life of 20 hours.
Step-by-step explanation:
The half-life of a drug is the amount of time it takes for half of the drug to be eliminated from the body. In this case, the drug has a half-life of 20 hours. To determine how many hours it would take for the drug to be eliminated (have less than 10% of the dose left), we can use the concept of half-life. After each half-life, the amount of drug remaining is halved. So, after one half-life (20 hours), the drug would have 50% of the original dose remaining. After two half-lives (40 hours), it would have 25% remaining. After three half-lives (60 hours), it would have 12.5% remaining. And so on. We can continue this pattern until we reach less than 10% of the original dose.
Let's do the calculations:
1st half-life: 50% remaining (20 hours)
2nd half-life: 25% remaining (40 hours)
3rd half-life: 12.5% remaining (60 hours)
4th half-life: 6.25% remaining (80 hours)
5th half-life: 3.125% remaining (100 hours)
6th half-life: 1.5625% remaining (120 hours)
So, it would take approximately 120 hours (or 5 days) for the drug to be eliminated, or have less than 10% of the dose remaining.