Question

After a plant or animal dies the 14C content decreases with a half-life of 5730 years. If an archaeologist finds an ancient firepit containing partially consumed firewood, and the 14C content of the wood is only 15.5% that of an equal carbon sample from a present-day tree, what is the age (in years) of the ancient site?

Answer 1

age of the site is 15411.75 years old

Step-by-step explanation:

Given data

plant or animal dies = 14C

time period = 5730 year

carbon = 15.5%

to find out

age (in years) of the ancient site

solution

we know that Final value = Initial value ×
`0.5^(n)`

here n is half life passed

so for 15.5%

15.5% = 100% of
`0.5^(n)`

0.155 = 1 ×
`0.5^(n)`

now take log both side

log 0.155 = log
`0.5^(n)`

n = log 0.155 / log 0.5

n = 2.68966

we know here 5730 years in half life

so for 2.68966 half-lives = 2.68966 × 5730 = 15411.7518

age of the site is 15411.75 years old