Answer:
3 half-lives have passed.
The bones are 17 190 years old.
Explanation:
The half-life of a radioactive element is the time required for the substance to lose half of its initial activity. In other words, the half-life is denoted by this symbol [tex]t_{\frac{1}{2} }[/tex]
Let's take the half-life of carbon as [tex]\frac{1}{2}[/tex]
After a certain number of years, the activity degenerates to half of the original activity. So it will be [tex]t_{\frac{1}{2} } = \frac{1}{2} *\frac{1}{2} \\ =\frac{1}{4}[/tex]
After some years, the activity will be [tex]\frac{1}{8}[/tex]
Thus three half-lives have passed. A simple formula to remember the pattern is to use the exponential expression :
[tex]\frac{1}{2} ^{x} = \frac{1}{8}[/tex]
solving for x gives x = 3
hence there half-lives.
For carbon, [tex]t_{\frac{1}{2} } = 5730 years[/tex]
since there half-lives have passed, the age of the sample will be [tex]t_{\frac{1}{2} } after three years = 5730 * 3\\ = 17 190 years[/tex]
The sample will be 17 190 years.
