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Carbon Dating The age of an ancient artifact can be deter-mined by the amount of radioactive carbon-14 remaining in it.If $D_{0}$ is the original amount of carbon-14 and $D$ is the amountremaining, then the artifact's age $A$ (in years) is given by$$A=-8267 \ln \left(\frac{D}{D_{0}}\right)$$Find the age of an object if the amount $D$ of carbon-14 thatremains in the object is 73$\%$ of the original amount $D_{0}$ .

$A \approx 2602$ years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:09

Carbon Dating The age of a…

00:59

The age of an ancient arti…

02:04

Carbon Dating The amount $…

02:06

Archaeology Carbon-14 is u…

01:57

Carbon-14 is present in al…

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Carbon dating is a method …

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It takes 5700 years for an…

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Radiocarbon Dating The amo…

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Archeologists can determin…

02:08

Radioactive carbon- 14 is …

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Carbon-14 is a radioactive…

Involve exponential decay.…

00:34

The usefulness of radiocar…

01:43

04:21

Carbon dating The half-lif…

01:15

An artifact originally had…

01:40

The amount of carbon- $14\…

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03:39

Archaeological samples are…

01:33

You have 5 grams of carbon…

So if you want to find the age well, we have to solve this equation for a And so what we know is that D is equal to 70% 73% of the original Dean on. So this is this d is equal 2.73 de not. And so we can plug this into our problem. Well, we have a is equal to is equal to negative 80 to 67 57 times the natural log of this this D which is 0.73 D not over D not. And so the d nods canceled. And so we're left with this 0.73 So if we plug this into our calculator, our age A is approximately. Let's say we have negative 80 to 67 times the natural laws of 0.73 And so this gives us approximately 26. 01 0.71 And so so this is our solution

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Carbon Dating The age of an ancient artifact can be determined by the amount…

The age of an ancient artifact can be determined by the amount of radioactiv…

Carbon Dating The amount $C$ in grams of carbon- 14 present in a certain sub…

Archaeology Carbon-14 is used to determine the age of artifacts in carbon da…

Carbon-14 is present in all living organisms and decays at a predictable rat…

Carbon dating is a method used to determine the age of a fossil or other org…

It takes 5700 years for an initial amount $A_{0}$ of carbon- 14 to break dow…

Radiocarbon Dating The amount $C$ in grams of carbon- 14 present in a certai…

Archeologists can determine the age of an artifact made of wood or bone by m…

Radioactive carbon- 14 is a substance found in all living organisms. After t…

Carbon-14 is a radioactive isotope used to date objects. If $A_{0}$ represen…

Involve exponential decay. Scientists dating a fossil estimate that $20 \%$ …

The usefulness of radiocarbon dating is limited to objects no older than 60,…

The usefulness of radiocarbon dating is limited to objects no older than 50,…

Carbon dating The half-life of $C-14$ is about 5730 yr.a. Archaeologists…

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The amount of carbon- $14\left(\begin{array}{c}6 \\ 3\end{array} \mathrm{C}\…

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