Question

a piece of fossilized tree trunk is possibly 4000 years old. The sample contains 65% of the original amount of carbon-14. Is the age correct?

Answer 1

Answer:

  no

Step-by-step explanation:

Let f represent the fraction of C-14 remaining as a function of the time t in years. Since the half-life of C-14 is about 5570 years, we have ...

  f = (1/2)^(t/5570)

Taking the log and solving for t, we get ...

  log(f) = (t/5570)log(1/2)

  5570·log(f)/log(1/2) = t

Filling in the given value for f, the value of t we get is ...

  5570·log(0.65)/log(0.5) = t ≈ 3462

It appears the estimate of 4000 years is a bit high.