Problem solving: If object has 1/12 original amt of radioactive carbon, estimate age.

[Lawrence]

The half-life of radioactive carbon is 5,730 years. Ordinary carbon, along with radioactive carbon (found naturally in a basically fixed ratio), is absorbed by all living things. This absorption stops at death. The radioactive carbon now begins to decay whilst the normal carbon does not. The ratio of the normal to radioactive carbon changes, and measurement of this is used to estimate the age of an object.

How old is an object if indications are that it has reduced to 1/12th of its original radioactive carbon? Round k to 6 decimal places.

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Does someone who knows how to answer this question?

 

[Ron Spain]

Exponents: Some number to the 5730th power is equal to 0.5, so...

Some number to the 5730th power is equal to 0.5 so what power of that same number equals 1/12?

 

[Deleted member 4993]

Some number to the 5730th power is equal to 0.5 so what power of that same number equals 1/12?

Let the number = n

n^(5730) = 1/2 = 2^(-1)

n = 2^(-1/5730)

n^x = 1/12

1/12 = 2^(-x/5730)

Take Log of both sides and solve for 'x'.

 

[stapel]

Does someone who knows how to answer this question?

Loads of us know how to answer this question. But we're not the student who needs to learn. So now it's time for you to try!

The half-life of radioactive carbon is 5,730 years. Ordinary carbon, along with radioactive carbon (found naturally in a basically fixed ratio), is absorbed by all living things. This absorption stops at death. The radioactive carbon now begins to decay whilst the normal carbon does not. The ratio of the normal to radioactive carbon changes, and measurement of this is used to estimate the age of an object.

How old is an object if indications are that it has reduced to 1/12th of its original radioactive carbon? Round k to 6 decimal places.

In the similar examples in your textbook and in your class notes (and online, such as here), you know that they used the continuous-growth formula they gave you, being something along the lines of this following:

. . . . .\(\displaystyle A\, =\, Pe^{kt}\)

...where "A" is the ending amount, "P" is the beginning amount, "k" is the growth (or decay) constant, and "t" is time.

So you took the given equation and plugged the given half-life info into it, solving for the value of "k". You wrote down at least six decimal places, or else stored that value in your calculator.

Then you returned to the given equation, and plugged the given 1/12 info into it, solving for the value of "t". And... then what? Where are you stuck?

Please be complete. Thank you!