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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

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Answer:

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

Step-by-step explanation:

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

[tex]P=P_{0}*e^{-dt}[/tex]

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:

[tex]P=10*e^{-0.00502*85}\\P= 6.5266 \mu g[/tex]

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

*Note that 0.502% = 0.00502.

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