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ryzh [129]
3 years ago
5

rehistoric cave paintings were discovered in a cave in France. The paint contained 34 % of the original​ carbon-14. Use the expo

nential decay model for​ carbon-14, Upper A equals Upper A 0 e Superscript negative 0.000121 t​, to estimate the age of the paintings.
Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

Answer:

Therefore the age of paint is 8915.78 years.

Step-by-step explanation:

Given that, the paint contain 34 % of the original carbon-14.

The exponential decay model for carbon-14 is

A=A_0e^{-0.000121t}

A= Remaining amount of carbon.

A_0 = initial amount of carbon.

Here A= 34% of A_0 =\frac{34}{100}A_0

\therefore \frac{34}{100}A_0=A_0e^{-0.000121t}

\Rightarrow \frac{34}{100}=e^{-0.000121t}

Taking ln both sides

\Rightarrow ln|\frac{34}{100}|=ln|e^{-0.000121t}|

\Rightarrow ln|\frac{34}{100}|={-0.000121t

\Rightarrow t=\frac{ln|\frac{34}{100}|}{-0.000121}

\Rightarrow t= 8915.78

Therefore the age of paint is 8915.78 years.

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