A toxic radioactive substance with a density of 9 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 55 years ago. If the half - life of the substance is 20 years, what was the density of the substance when it was deposited 55 years ago?

60.5 milligrams per square centimeter First, determine how many half lives have expired by dividing the time by the half-life. So: 55/20 = 2.75 That means that only 2^ (-2.75) = 0.148650889 = 14.8650889% of the original substance remains. So just divide the amount remaining by 0.148650889 to get the original amount. 9 / 0.148650889 = 60.5445419 So originally, there was 60.5 milligrams per square centimeter 55 years ago.