SOLUTION: the half life of carbon14 is 5730 years. A.) f(t)=ae^(-kt) solve for k b.) if the bone is 65% of the original amount of carbon14. how old is the bone in years? c.) If a bo

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: the half life of carbon14 is 5730 years. A.) f(t)=ae^(-kt) solve for k b.) if the bone is 65% of the original amount of carbon14. how old is the bone in years? c.) If a bo      Log On


   

Question 1071963: the half life of carbon14 is 5730 years.
A.) f(t)=ae^(-kt) solve for k
b.) if the bone is 65% of the original amount of carbon14. how old is the bone in years?
c.) If a bone is known to be 1900 years old, what percent of the original Carbon14 is remaining in the bone. Round to the nearest percent.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
A:
Find k, given half-life 5730 years.
1%2F2=1%2Ae%5E%28k%2A5730%29
ln%281%2F2%29=ln%28e%5E%28k%2A5730%29%29
ln%281%2F2%29=5730%2Ak
k=ln%281%2F2%29%2F5730
highlight%28k=-0.000121%29

B:
How old is bone if 65% of original C-14 remains?
0.65=1%2Ae%5E%28-0.000121%2At%29
ln%280.65%29=ln%28e%5E%28-0.000121t%29%29
-0.000121t=ln%280.65%29
t=ln%280.65%29%2F%28-0.000121%29
highlight%28t=3560%29, years