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The half life of carbon 14 is 5,730 year suppose a fossil found with 20 percent as much of its carbon 14 as compared to a living sample how old is the fossil

3,235 years
32,346 years
1331 years
13,307 years

Respuesta :

13,307 I know because I do this type of math and I fell your pain but I asked someone else this question that’s why I don’t know step bye step but yeah hope this help
Trancescient

13,305 years

Step-by-step explanation:

[tex]A = A_02^{-\frac{t}{5730}}[/tex]

Since only 20% of the original C-14 is left, then [tex]A=0.2A_0[/tex]. We can then write

[tex]0.2A_0=A_02^{-\frac{t}{5730}}[/tex]

Taking the log of both sides,

[tex]\log 0.2 = \left(-\dfrac{t}{5730}\right)\log 2[/tex]

Solving for t,

[tex]t = \dfrac{-(5730\:\text{years})\log 0.2}{\log 2}[/tex]

[tex]\:\:\:\:\:\:\:= 13,305\:\text{years}[/tex]

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