Question

Situation:

A hiker in Africa discovers a skull that
contains 51% of its original amount of C-
14.
N=Noekt
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 skull to the nearest year.
Enter the correct answer.

Answer 1

Explanation:

To determine the age of the skull, we can use the equation for radioactive decay:

N = N0 * e^(-kt)

where N is the remaining amount of C-14, N0 is the initial amount of C-14, k is the decay constant, and t is the time elapsed.

In this situation, we know that N = 0.51N0 (since the skull contains 51% of its original amount of C-14) and k = 0.0001. Plugging these values in, we get:

0.51N0 = N0 * e^(-0.0001t)

Simplifying, we can divide both sides by N0 to get:

0.51 = e^(-0.0001t)

Taking the natural log of both sides, we get:

ln(0.51) = -0.0001t

Solving for t, we get:

t = -ln(0.51)/0.0001

t ≈ 3,841 years

Therefore, the age of the skull is approximately 3,841 years old.