# 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?

After ten half lives, there will be $\frac{1}{1024}$ left. This will be less than 0.1 mg. It will take 40 hours for 10 half lives.
After 20 half lives. there will be about $\frac{1}{1000000}$ 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.