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

Compounded continuously model are evaluated using exponential functionsThere are 8.177 bacteria left after 40 daysThe given parameters are:[tex]\mathbf{a = 10}[/tex] --- the initial number of bacteria[tex]\mathbf{r = 0.502\%}[/tex] --- the decay rate[tex]\mathbf{n = 40}[/tex] --- the number of daysThe amount of bacteria left each day is calculated using:[tex]\mathbf{T_n = a \times (1 - r)^n}[/tex]So, we have:[tex]\mathbf{T_{40} = 10 \times (1 - 0.502\%)^{40}}[/tex]Express percentage as decimal[tex]\mathbf{T_{40} = 10 \times (1 - 0.00502)^{40}}[/tex]Simplify the expression in bracket[tex]\mathbf{T_{40} = 10 \times 0.99498^{40}}[/tex]Evaluate[tex]\mathbf{T_{40} = 8.1766}[/tex]Approximate[tex]\mathbf{T_{40} = 8.177}[/tex]Hence, there are 8.177 bacteria left after 40 daysRead more about compounded continuously model at: