SOLUTION: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 12% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 12% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)      Log On


   

Question 1153002: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 12% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
y=pe%5E%28kx%29
1%2F2=1%2Ae%5E%285730k%29
1%2F2=e%5E%285730k%29
ln%281%2F2%29=5730k
-ln%282%29=5730k
k=-ln%282%29%2F5730
k=-0.000120968
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y=pe%5E%28-0.000120968x%29
You want to find x for p=100 and y=12.

Taking logarithms of right and left sides,
and a few algebra steps:

x=%28ln%2812%29-ln%28100%29%29%2F%28-0.000120968%29

highlight%28x=%28ln%28100%29-ln%2812%29%29%2F0.000120968%29
Compute, and do the rounding that you need.