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
[tex]A=A_0e^{-0.000121t}[/tex]
A= Remaining amount of carbon.
[tex]A_0[/tex] = initial amount of carbon.
Here A= 34% of [tex]A_0[/tex] [tex]=\frac{34}{100}A_0[/tex]
[tex]\therefore \frac{34}{100}A_0=A_0e^{-0.000121t}[/tex]
[tex]\Rightarrow \frac{34}{100}=e^{-0.000121t}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|\frac{34}{100}|=ln|e^{-0.000121t}|[/tex]
[tex]\Rightarrow ln|\frac{34}{100}|={-0.000121t[/tex]
[tex]\Rightarrow t=\frac{ln|\frac{34}{100}|}{-0.000121}[/tex]
[tex]\Rightarrow t= 8915.78[/tex]
Therefore the age of paint is 8915.78 years.
