th​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 6565​% of the​ carbon-14 expected in living​ matter, w

Question

i really need help with this question I have been struggling for it for a while

Answer 1

T = half-life = 5600 years

 

I assume the problem statement has a typo and you really meant 65%, not 6565%.

 

I suppose you want the age of the charcoal in years.  Call it t.  If 65% of the carbon 14 remains, then the amount left is 0.65 times the initial amount A₀.

 

0.65A₀ = A₀(1/2)^t/T

 

0.65 = (0.5)^t/5600

 

ln(0.65) = (t/5600) ln(0.5)

 

t = 5600 ln(0.65) / ln(0.5) ≅ 3480 years