The age of an ancient tree trunk is estimated using radiocarbon dating. If the trunk has a C-14 decay rate that is 34% of what it is in living plants, how old is the trunk? The half-life of C-14 is 5730 years.

8923 years

Step-by-step explanation:

Half life of C-14 = 5730yrs

decay rate = 34%

Halt life (t^1/2) = (ln2) / k

5730 = (ln2) / k

k = (ln2) / 5730

k = 1.209 * 10^-4

For first order reaction in radioactivity,

ln (initial amount) = - kt

ln (34/100) = - (1.209*10^-4) t

-1.0788 = - (1.209*10^-4) t

t = - 1.7088 / - 1.209*10^-4

t = 8923 years