Question

Situation:

An archaelogist in Turkey discovers a
spear head that contains 32% 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

13,093 years

Explanation:

N = N0 e -kt . Here, N = 27 % of N0 = 27/100(N0 ) , k = 0.0001, then 27/100N0 = N0 e-0.001t .

Therefore, 0.27 = e-0.001t .On taking natural logarithms of both the sides, we get - 0.001t ln e = ln 0.27 ( log ab = b log a), or, - 0.001t = -1.30933332 ( as ln e = 1).

Therefore, t = 1.30933332/ 0.0001 = 13093.33 years = 13093 years on rounding off to the nearest year.