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