Question

Situation:

An archaelogist in Turkey discovers a
spear head that contains 53% of its
original amount of C-14.
N = Noe-kt
No inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Find the age of the spear head to the nearest
year.

Answer 1

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.