Answer
Explanation
The weight (W kg) of a decaying radio active substance after n years is given by:
[tex]\begin{gathered} W=W_0(\frac{1}{2})^{\frac{n}{100}} \\ \text{Where }W_0kg\text{ is the initial weight of the substance.} \end{gathered}[/tex]To find the number of years for the radioactive substance to decay to half of its initial weight, it implies the weight of the substance at that number of years will be:
[tex]W=\frac{1}{2}W_0[/tex]Therefore,
[tex]\begin{gathered} \frac{1}{2}W_0=W_0_{}(\frac{1}{2})^{\frac{n}{100}} \\ \text{Divide both sides by W}_0 \\ (\frac{1}{2})^1=_{}(\frac{1}{2})^{\frac{n}{100}} \\ Equate\text{ the exponents} \\ 1=\frac{n}{100} \\ n=1\times100 \\ n=100\text{ years} \end{gathered}[/tex]