SOLUTION: Hello tutor I really need your help solving this The half-life of carbon 14 is 5730 years. How old is a bone containing 20% of its original carbon 14?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello tutor I really need your help solving this The half-life of carbon 14 is 5730 years. How old is a bone containing 20% of its original carbon 14?      Log On


   

Question 969137: Hello tutor I really need your help solving this
The half-life of carbon 14 is 5730 years. How old is a bone containing 20% of its original carbon 14?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y=pe%5E%28-kt%29
p, initial amount
y, final amount
k, a decay constant
t, time in years

k for the half-life:
1%2F2=e%5E%28-kt%29
ln%281%2F2%29=-kt
k=-ln%281%2F2%29%2Ft
k=ln%282%29%2Ft
Given half life 5730 years.
k=0.693147%2F5730=highlight%281.210%2A10%5E-4%29-------fixed earlier mistake.

What if y=20% of p?
0.2=e%5E%28-0.0001210%2At%29
ln%280.2%29=-0.0001210%2At
t=ln%280.2%29%2F%28-0.0001210%29
highlight%28t=ln%285%29%2F0.0001210%29