A fossilized leaf contains 35% 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.
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The half-life of a substance is the time it takes for half of the substance to decay. In this case, the half-life of carbon 14 is 5600 years. This means that after 5600 years, half of the carbon 14 in a sample will have decayed.
The formula for calculating the age of a fossil based on the amount of carbon 14 remaining is:
t = (half-life) * log2(N0/N)
where:
t is the age of the fossil,
N0 is the original amount of carbon 14,
N is the remaining amount of carbon 14.
In this case, N0 is 100% (the original amount of carbon 14), and N is 35% (the remaining amount of carbon 14). Plugging these values into the formula gives:
t = 5600 * log2(100/35)
Using a calculator, we find that log2(100/35) is approximately 1.51. Therefore:
t = 5600 * 1.51 = 8456 years
So, the fossil is approximately 8456 years old. Rounding to the nearest year gives an age of 8456 years.
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