SOLUTION: Question: A bone was found to contain 40% of the Carbon-14 that it contained when it was part ofa living animal. If the decay of Carbon-14 is exponential with an annual rate of dec
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Question 1164123: Question: A bone was found to contain 40% of the Carbon-14 that it contained when it was part ofa living animal. If the decay of Carbon-14 is exponential with an annual rate of decay of 0.0124%, how long ago did the animal die?
How far I got:
The amount lost was 60% or 0.6
Rate is -0.0124% or -0.000124
Equation created: 0.6 = 1e^-0.000124t | t is the number of years
I get an answer: -14694.5065 meaning the animal died 14695 year ago
Apparantly I am wrong by one digit, the answer being 1471 years.
Where did I insert the extra 0?
Thank you
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Nothing you wrote is even remotely correct.
Decay rate of Carbon-14 is -0.0121% or -0.000121.
Does NOT yield the amount lost, it yields the amount remaining, therefore
)
}{-0.000121}\ \approx\ 7600\text{ years})
Note that 1471 years is about 25% of a half-life of 5730 years, after 1471 years you would have about 84% remaining. 40% remaining after 7600 years makes sense because 40% is between 50% and 25% which occur at 5730 and 11460 years respectively.
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.
On radioactive Carbon-14 dating, see and learn from the lessons
- Using logarithms to solve real world problems
- Radioactive decay problems
- Carbon dating problems
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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