Answer:
Option (2)
Step-by-step explanation:
Formula to determine the final amount of an element after t years is,
[tex]A_t=A_0e^{kt}[/tex]
where [tex]A_t[/tex] = Final amount
[tex]A_0[/tex] = Initial amount
t = Duration or time
k = decay constant
If the half life period of a C-14 isotope = 5730 years
[tex]A_t=\frac{A_0}{2}[/tex] [For half life period]
[tex]\frac{A_0}{2}=A_0e^{(5730)k}[/tex]
[tex]e^{5730k}=0.5[/tex]
[tex]\text{ln}(e^{5730k})=\text{ln}(0.5)[/tex]
0.5730k = -0.6931
k = [tex]-\frac{0.6931}{5730}[/tex] = -0.000121
Therefore, formula for the radioactive decay will be.
[tex]A_t=A_0e^{-0.000121t}[/tex]
Option (2) will be the answer.
