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?

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.