Answer:
16,383.33 years ( approx )
Step-by-step explanation:
Given equation that shows the amount of carbon-14 after t years,
[tex]y = y_0 e^{-0.00012t}[/tex]
Where,
[tex]y_0[/tex] = initial amount,
∵ 14% of [tex]y_0[/tex] = [tex]\frac{14}{100}y_0[/tex] = [tex]\frac{7}{50}y_0[/tex]
[tex]\frac{7}{50}y_0= y_0 e^{-0.00012t}[/tex]
[tex]\frac{7}{50}=e^{-0.00012t}[/tex]
Taking ln both sides,
[tex]\ln(\frac{7}{50})=-0.00012t[/tex]
[tex]-1.966=-0.00012t[/tex]
[tex]\implies t =\frac{-1.966}{-0.00012}=16383.33[/tex]
Hence, the painting would be 16383.33 years old ( approx )
