SOLUTION: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 26% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 26% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)      Log On


   

Question 1128145: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 26% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)
Answer by greenestamps(13198) About Me  (Show Source):
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If x is the number of half lives, then the fraction remaining is .5%5Ex.

.5%5Ex+=+.26
x%2Alog%28%28.5%29%29+=+log%28%28.26%29%29
x+=+log%28%28.26%29%29%2Flog%28%28.5%29%29 = 1.943416472 to several decimal places.

The age of the fossil is then 5730%2A1.943416472+=+11136 to the nearest whole number.

ANSWER: the age of the fossil is 11136 years.