Question

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 45 years ago if the half life of the substance is 20 years what was the density of the substance when it was deposited 45 years ago

Answer 1

  Think about what a half-life means as a table.

years amount Left

20 1/2

40 1/4

60 1/8

80 1/16

Starting at t = 0, the amount left (or density) = (1/2)^(t/20)

For t =35, the decay factor = .297

Since you need to work backwards, divide by that factor.  6 / .297 = 20.18 mg per sq cm