An Anthropologist finds bones that her Instruments measure it as 0.921% of the amount of carbon- 14 the bones would have contained when the person was alive. How long ago did the person die?
The half life, t 1/2, carbon 14 is 5,730 years. Round To the nearest thousands
1(1/2)^(t/5730) = .921
.5^(t/5730) = .921
take log of both sides and use log rules ...
(t/5730) log .5 = log .921
take over
I Need The Answer What The Answer
To determine how long ago the person died, we can use the concept of half-life. Carbon-14 has a half-life of 5,730 years, which means that after 5,730 years, half of the initial amount of carbon-14 will decay.
In this case, the anthropologist has measured the amount of carbon-14 in the bones compared to what it would have contained when the person was alive. The measured amount is 0.921% of the original amount.
To calculate the time that has passed since the person's death, we can use the following formula:
t = (t1/2 / 0.693) * log(N0/Nt)
Where:
t = time elapsed since death
t1/2 = half-life of carbon-14 (5,730 years)
N0 = initial amount of carbon-14
Nt = measured amount of carbon-14
Let's plug in the known values:
t = (5,730 / 0.693) * log(1 / 0.00921)
To find the logarithm, we can use a calculator or a logarithm table. Calculating the logarithm of 0.00921 (or log(1/0.00921)) will give us the value -2.036.
t = (5,730 / 0.693) * (-2.036)
Simplifying further:
t = 8,267.67 years
Rounding to the nearest thousands as stated in the question, we find that the person died approximately 8,268 years ago.