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Use -0.000121 as the decay constant for Carbon 14.An ancient wood fork-like instrument was found to have $3 \%$ of the amount of Carbon 14 that a new one would have, how old is the fork?

29,062.5 years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:50

Use -0.000121 as the decay…

02:27

Old Clothes If only $15 \%…

02:57

Use the radioactive decay …

01:57

The decay of Carbon-14 fol…

01:15

If radioactive Carbon 14 h…

02:06

Archaeology Carbon-14 is u…

02:13

Carbon- 14 Dating. Only $1…

02:52

Use the exponential decay …

A wooden artifact from an …

00:56

Deal with radioactive deca…

03:01

These exercises use the ra…

Involve exponential decay.…

working with carbon 14, that has a decay constant of negative 0.1 to one. Supposing that 3% of the amount of carbon 14 was just found that 3% of the amount that a new um fork like instrument looks like we're working with. What have we wanna know, How old is this fork? So I've gone ahead and calculated that half life for us using this formula right here. So we have a half life of 5745 years. And now all we need to do is use this elapsed time formula. So we have our half life which is obviously 5745 years, multiplying that by the log of our beginning amount divided by our ending amount. We're working with percentages. So I've gone ahead and assume that obviously it started with 100% of this carbon 14 substance, Dividing that by our ending amount, which is now only 3% of the substance. That thing gets divided by the log of two. And then it's pretty straightforward to just plug that into our calculators. And we can see that this Fork like instrument is about 29,062 years old. It's a .5 so 29,062 and a half years old.

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