Answer:
Age of the spear head = 6349 years.
Step-by-step explanation:
Expression to be used to calculate the age of the spear head,
[tex]N_t=N_0e^{-kt}[/tex]
Here, [tex]N_t[/tex] = Final amount of C-14
[tex]N_0[/tex] = Initial amount
[tex]k[/tex] = 0.0001
[tex]t[/tex] = Time in years
If [tex]N_t[/tex] = 53% of [tex]N_0[/tex] = [tex]N_0\times (0.53)[/tex]
[tex]0.53N_0=N_0e^{-0.0001\times t}[/tex]
[tex]0.53=e^{-0.0001t}[/tex]
[tex]\text{ln}(0.53)=\text{ln}(e^{-0.0001t})[/tex]
[tex]-0.634878=(-0.0001)t[/tex]
[tex]t=6348.78[/tex] years
[tex]t[/tex] ≈ [tex]6349[/tex] years
Therefore, age of the spear head = 6349 years.
