Question

a hiker in africa discovers a skull that contains 41% of its original amount of c-14. find the age of the skull to the nearest year

Answer 1

9514 1404 393

Answer:

  7371 years

Step-by-step explanation:

The half-life of Carbon-14 is reportedly about 5730 years. Then the exponential decay equation can be written as ...

  f = (1/2)^(t/5730)

where f is the fraction remaining after t years.

Taking logarithms and solving for t, we find ...

  log(f) = (t/5730)log(1/2)

  t = 5730·log(f)/log(1/2)

For the fraction f = 0.41, the age is approximately ...

  t = 5730·log(0.41)/log(1/2) ≈ 5730·1.286304 ≈ 7371 . . . years

The age of the skull could be estimated to be 7371 years.