Answer:
The painting area is approximately 28980 years old.
Step-by-step explanation:
The model for the amount of carbon-14 after t years is given by:
[tex]A(t) = A(0)e^{-0.000121t}[/tex]
In which A(0) is the original amount.
The paint contained 3% of the original carbon-14.
This means that [tex]A(t) = 0.03A(0)[/tex]. This means that we have to find t.
[tex]A(t) = A(0)e^{-0.000121t}[/tex]
[tex]0.03A(0) = A(0)e^{-0.000121t}[/tex]
[tex]e^{-0.000121t} = 0.03[/tex]
[tex]\ln{e^{-0.000121t}} = \ln{0.03}[/tex]
[tex]-0.000121t = \ln{0.03}[/tex]
[tex]t = -\frac{\ln{0.03}}{0.000121}[/tex]
[tex]t = 28980[/tex]
The painting area is approximately 28980 years old.
