Question

Alexander Litvinenko was poisoned with 10 micrograms of the radioactive substance Polonium-210. Since radioactive decay follows a compounded continuously model, we can determine the amount of substance left in Alexander Litvinenko's body at any given time. If Polonium-210 has a decay rate of .502%, then determine the amount of Polonium-210 left in his body after 85 days

Answer 1

There will be 6.5266 micrograms of Polonium-210 in his body after 85 days.

Explanation:

A continuously compounded decay can be modeled by the following expression:

`P=P_(0)*e^(-dt)`

Where "P" is the amount of Polonium-210 left after "t" days, "P0" is the initial amount of Polonium-210 and "d" is the decay rate. Replacing the known values into the expression yields:

`P=10*e^(-0.00502*85)\\P= 6.5266 \mu g`

There will be 6.5266 micrograms of Polonium-210 in his body after 85 days.

*Note that 0.502% = 0.00502.