Question

rehistoric cave paintings were discovered in a cave in France. The paint contained 34 % 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​, to estimate the age of the paintings.

Answer 1

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.