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Prehistoric cave paintings were discovered in a cave in France. The paint contained 10 %10% of the original​ carbon-14. Use the exponential decay model for​ carbon-14, Upper A equals Upper A 0 e Superscript negative 0.000121 t=A0e−0.000121t​, to estimate the age of the paintings.

Respuesta :

whitneytr12

Answer:

t=19188.2 y

Step-by-step explanation:

The exponential decay equation is:

[tex] A=A_{0}e^{-0.00012t}[/tex]      (1)

But, A is 10% of A₀, it means that A=0.10A₀.

If we put it into equation (1), we will have:

[tex] 0.10A_{0}=A_{0}e^{-0.00012t}[/tex]      

[tex] 0.10=e^{-0.00012t}[/tex]         (2)

Now, we just need to solve (2) for t.

[tex] t=\frac{ln(0.10)}{-0.000121} = 19188.2 y [/tex]      

I hope it helps you!    

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