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