SOLUTION: Hi, I'm trying to study a study guide that my teacher gave me but I just don't understand how he got the answer. The problem is A fossilized leaf contains 28% of its normal amoun

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, I'm trying to study a study guide that my teacher gave me but I just don't understand how he got the answer. The problem is A fossilized leaf contains 28% of its normal amoun      Log On


   



Question 324566: Hi, I'm trying to study a study guide that my teacher gave me but I just don't understand how he got the answer. The problem is
A fossilized leaf contains 28% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.
What is the formula?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N=N0%2Ae%5E%28kt%29
To find k, use the half life information.
%281%2F2%29N0=N0%2Ae%5E%28kt%29
e%5E%28k%285600%29%29=1%2F2
5600k=ln%281%2F2%29
k=ln%281%2F2%29%2F5600
k=-1.238x10%5E%28-4%29
Work the problem in the same way.
Instead of (1/2) of the original carbon, you have 28% or 0.28 times the original amount.
Find t.
0.28N0=N0e%5E%28kt%29
e%5E%28kt%29=0.28
kt=ln%280.28%29
t=ln%280.28%29%2F%28-1.238x10%5E%28-4%29%29
t=-1.273%2F%28-1.238x10%5E%28-4%29%29
t=10284
10284 years old.