Question

A toxic radioactive substance with the density of 4 mg/cm² is detected in the been detected in the ventilating ducts that was used 35 years ago. if the half-life of substances 20 years what is the density of a substance when it was deposited 35 years ago

Answer 1

The formula for half-life is:

$A = P(0.5)^{t/h}$

A is the amount remaining, P is the initial amount, t is the time that has passed, and h is the half-life of the substance.  Plug in the values that you know and solve:

$4 = P(0.5)^{35/20} \\ \\ 4 = P(0.5)^{1.75} \\ \\ P = \frac{4}{0.5^{1.75}} \\ \\ P \approx 13.4543426441$

Rounded to the nearest whole number, the density of the substance was about 13mg / cm².