Question

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?

Answer 1

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