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 40 days. Provide 3 decimal places and units in your answer.

Answer 1

Compounded continuously model are evaluated using exponential functions

There are 8.177 bacteria left after 40 days

The given parameters are:

$\mathbf{a = 10}$ --- the initial number of bacteria

$\mathbf{r = 0.502\%}$ --- the decay rate

$\mathbf{n = 40}$ --- the number of days

The amount of bacteria left each day is calculated using:

$\mathbf{T_n = a \times (1 - r)^n}$

So, we have:

$\mathbf{T_{40} = 10 \times (1 - 0.502\%)^{40}}$

Express percentage as decimal

$\mathbf{T_{40} = 10 \times (1 - 0.00502)^{40}}$

Simplify the expression in bracket

$\mathbf{T_{40} = 10 \times 0.99498^{40}}$

Evaluate

$\mathbf{T_{40} = 8.1766}$

Approximate

$\mathbf{T_{40} = 8.177}$

Hence, there are 8.177 bacteria left after 40 days

Read more about compounded continuously model at:

https://brainly.com/question/73731