Answer:
Value of the decay constant k = 0.00012
Step-by-step explanation:
Formula to determine the age of the fossils by C-14 decay is given as
[tex]A_{t}=A_{0}e^{-kt}[/tex]
where A(t) = C-14 remaining after t years
A0 = original amount of C-14
K = decay constant
t = time taken for decay
Now we have to calculate the value of constant k when half life of C-14 is given as 5730 years.
Since half life has been given therefore final amount after 5730 years will be A/2 and initial amount will be A.
Now the equation becomes as
[tex]\frac{A}{2}=Ae^{(-k)(5730)}[/tex]
[tex]\frac{1}{2}=e^{-5730k}[/tex]
Now by taking natural log on both the sides
[tex]ln(\frac{1}{2})=ln(e^{-5730k})[/tex]
ln 1 - ln2 = -5730k (since lne = 1)
0 - ln2 = -5730k
[tex]0.63915=5730k[/tex]
k = 0.00012
Therefore k = 0.00012 is the answer.
