SOLUTION: In order to determine the age of a piece of wood, the amount of carbon-14 was measured. It was determined that the wood had lost 33.1% of its carbon-14. How old is this piece of wo

Question 1149491: In order to determine the age of a piece of wood, the amount of carbon-14 was measured. It was determined that the wood had lost 33.1% of its carbon-14. How old is this piece of wood?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

If 33.1% has been lost, 66.9% remains. So we need to know how many half-lives have passed if 66.9% of the Carbon-14 remains.

x = 0.57992... or approximately 0.58.

You didn't give the half-life of Carbon-14, so we can't get a final answer. Multiply the half-life in years by 0.58 to find the age of the piece of wood in years.

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For tutor @ikleyn....

Something is wrong somewhere in your calculations. 10000 years is more than the half life; 66.9% will not still remain....

Answer by ikleyn(52765)   (Show Source): You can put this solution on YOUR website!
.

Carbon (C) has three naturally occurring isotopes. Both C-12 and C-13 are stable, but C-14 is radioactive
and decays to nitrogen-14 with a half-life of approximately 5,730 years. Naturally occurring radiocarbon is
produced as a secondary effect of cosmic-ray bombardment of the upper atmosphere. Plants transpire
to take in atmospheric carbon, which is the beginning of absorption of carbon into the food chain.

As long as the plant is alive, the ratio of C-14 to C-12 in its body remains constant.
After the plant dies, carbon-14 continues to decay without being replaced.

The current amount of radioactive Carbon-14 present in the remains of the plant can be measured,
and the ratio of the current amount of Carbon-14 to its initial amount can be used to determine age.
The last ratio is described by the function C(t) = 0.5^(t/5730), where "t" is time (in years).

Since 33.1% of Carbon-14 is lost, 66.9% is remained, or 0.669 of its initial amount. Thus, you should solve an equation C(t) = 0.669, which is y = = , for unknown t. Take logarithm base 10 from both sides. You get an equation = . Apply the Power Rule to the logarithm. You get an equation . Therefore, = = 3323 years. ANSWER. The piece of wood is about 3323 years old.

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Solved.

The letter which you see cut in all formulas, is the letter "t", symbolizing time.

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There is a group of lessons in this site, which covers all these and similar problems
    - Using logarithms to solve real world problems, and
    - Solving problem on Newton Law of cooling

So, if somebody wants to learn on how to solve such problem, he (or she) has good source to read from.

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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