Question

If you have 100mg of a drug with a half-life of 4 hours, how long will it take to totally eliminate it from the body?

Answer 1

Technically it will take forever as dividing by 2 will always leave a remainder. But the effective amount remaining will be less than 1 mg after 40 hours.

Explanation:

After ten half lives, there will be `1/1024` left. This will be less than 0.1 mg. It will take 40 hours for 10 half lives.

0.1 mg will probably have no effect so practically the drug is no longer affecting the body.

After 20 half lives. there will be about `1/ 1000000` left. this will take 80 hours. At this point the drug can certainly be considered to be gone. However in reality there is a small amount of drug left.