Answer:
To find the age of the spear head, we can use the formula for radioactive decay:
N = Noe^(-kt)
where N/No is the fraction of the original amount of C-14 remaining after time t. We know that N/No = 0.53, k = 0.0001, and we want to solve for t.
0.53 = e^(-0.0001t)
Taking the natural logarithm of both sides, we get:
ln(0.53) = -0.0001t
Solving for t, we get:
t = -ln(0.53)/0.0001 ≈ 3,760 years
Therefore, the age of the spear head is approximately 3,760 years.