We need to find how much will be left after 6 half-lives of a radioactive isotope starting with 130g.
One way to write the amount N of radioactive isotope left after a time t, with an initial amount N₀ and a half-life τ is:
[tex]N=N_0\left(\frac{1}{2}\right)^{t\text{ /}\tau}[/tex]
Notice that when t = τ, we have:
[tex]N=\frac{N_0}{2}[/tex]
In this problem, we have:
[tex]\begin{gathered} N_0=130g \\ \\ t=6\tau \end{gathered}[/tex]
Then, we obtain:
[tex]N=130g\left(\frac{1}{2}\right)^{6\tau\text{ /}\tau}=130g\left(\frac{1}{2}\right)^6=\frac{130g}{64}\cong2\text{ g}[/tex]
Therefore, rounding to the nearest gram, the answer is 2 grams.
