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Use -0.000121 as the decay constant for Carbon 14.If an ancient wooden axe handle is found to have one-tenth the amount of Carbon 14 that a new one would have, how old is the axe handle?

19,030 years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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The carbon-14 decay rate o…

Given that the decay constant is negative 0.001-1. If 1/10 of the substance has been found on some ancient ancient piece of that was just discovered. How old is that particular piece? And we're working with carbon 14 right here. So you can see that I've got the formulas for us over here. Let's first start by finding the half life going ahead and just plugging in the decay constant into K. For the bottom there we see that we've got a half life Of carbon 14 which is equal to 5745 years. This will allow us to then use this top formula for this elapsed time, which is what we're looking for. Starting with the half life of the substance which is 5745 years. Then multiply that by the log of our beginning amount, which in this case I am just using Um%ages. 100 of this and we now only have 10% of this. So the beginning amount would have been 100% of the substance. We now only have 10% of the substance. And then that gets divided by the log of two. Let's go ahead then and calculate that what we get is an elapsed time, which is equal to 19,000 84 years .47 We want to be specific. So just over 19,000 years have passed.

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