Answer:
2772.5 years
Explanation:
Using the equation for radioactive decay of material:
[tex]ln \frac{N}{N_{o} } = -k*t[/tex]
Where:
N is the amount of the material at time t, [tex]N_{o}[/tex] is the original amount of the material, and k is the rate constant.
The value if the rate constant (k) = 0.693/[tex]t_{1/2}[/tex]
Where:
[tex]t_{1/2}[/tex] is the half life = 5730 years.
Then k = 0.693/5730 = 0.000121 (1/year)
Then solving for 't', we have:
[tex]ln\frac{71.5}{100} = -0.000121*t[/tex]
t = -0.3355/-0.000121 = 2772.5 years
Therefore, the wooden boat is 2772.5 years old.
