A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 45 years ago. If the half-life is 20 years, what was the density of the substance when it was deposited 45 years ago?
For this case we have an equation of the form: y = A * (b) ^ t Where, A: initial amount b: decrease rate t: time in years. Substituting values we have: 7 = A * (0.5) ^ ((1/20) * t) For t = 45 years we have: 7 = A * (0.5) ^ ((1/20) * 45) Clearing A: A = 7 / ((0.5) ^ ((1/20) * 45)) A = 33.3 Answer: the density of the substance when it was deposited 45 years ago was: A = 33.3 milligrams per square centimeter
