Question

Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (Polonium-210 in this case) each day. If you begin with 258 mg of Bismuth-210, how much remains after 7 days?

Answer 1

In this problem, we have an exponential decay function of the form

`y=a(1-r)^x`

where

y is the remaining Bismuth 210 in mg

x is the number of days

a is the initial value

r is the rate of decay

so

we have

a=258 mg

r=13%=13/100=0.13

x=7 days

substitute

`\begin{gathered} y=258(1-0.13)^7 \\ y=97.33\text{ mg} \end{gathered}`