A support pole for an ancient structure is found to have one-fifth of the carbon-14 of a modern, living tree. How long ago did the tree used to make the support pole die? Give your answer to the nearest whole number.
poor example!
To determine how long ago the tree used to make the support pole died, we can use the half-life of carbon-14. The half-life of carbon-14 is approximately 5730 years.
Since the support pole has one-fifth the amount of carbon-14 as a modern, living tree, it means that its carbon-14 content has undergone 1 half-life of decay.
To find out the time it takes for one half-life, we divide the half-life by the natural logarithm of 2 (ln 2 ≈ 0.6931).
Therefore, the time it takes for one half-life is approximately 5730 years / 0.6931 ≈ 8267 years.
Therefore, the tree used to make the support pole died approximately 8267 years ago.
To determine how long ago the tree used to make the support pole died, we need to understand the concept of carbon-14 dating.
Carbon-14 is an isotope of carbon that is present in the Earth's atmosphere in a constant ratio with carbon-12. Living organisms, including trees, constantly exchange carbon with the environment through processes like photosynthesis. When an organism dies, it no longer exchanges carbon with the environment, and the amount of carbon-14 it contains gradually decreases over time due to radioactive decay.
The half-life of carbon-14 is approximately 5730 years, which means that after this period, half of the carbon-14 in a sample will have decayed. By measuring the current ratio of carbon-14 to carbon-12 in a sample and comparing it to the known ratio in living organisms, scientists can estimate the age of the sample.
In this case, the support pole has one-fifth of the carbon-14 of a modern, living tree. This suggests that the carbon-14 in the support pole has decayed by four-fifths (1 - 1/5) or 80%.
Since the half-life of carbon-14 is 5730 years, we can calculate the approximate age of the support pole by determining how many half-lives would be required for the carbon-14 to decay by 80%.
80% decay corresponds to 3 half-lives (50% per half-life), as 50% + 25% + 12.5% = 87.5%, which is more than 80%.
Therefore, we can estimate that the tree used to make the support pole died approximately 3 half-lives ago. Multiplying 5730 years (the half-life) by 3 gives us an approximate age of 17,190 years.
Rounding to the nearest whole number, we can conclude that the tree used to make the support pole died approximately 17,000 years ago.
look up the half-life of carbon 14 (it's around 5400 yrs)
(1/2)^(time / half-life) = 1/5
(time / half-life) * log(1/2) = log(1/5)