Answer:
We have to determine the time it takes for carbon 14 to decay to 15% of its original amount.
The half life of carbon 14 is 5,730 years
elapsed time = half life * log (beginning amount / ending amount) / log 2
elapsed time = 5,730 * log (100 / 15) / log 2
elapsed time = 5,730 * 0.82390874094 / 0.30102999566
elapsed time = 5,730 * 2.7369655942
elapsed time = 15,683 years
= 15,700 years
Step-by-step explanation:
Solving the exponential equation, it is found that the painting is 15,679 years old.
The amount of carbon-14 after t years is modeled by the following equation:
[tex]A(t) = A(0)e^{-0.000121t}[/tex]
It retains 15% of the original amount, thus:
[tex]A(t) = 0.15A(0)[/tex]
Solving for t, we find the age.
[tex]0.15A(0) = A(0)e^{-0.000121t}[/tex]
[tex]e^{-0.000121t} = 0.15[/tex]
[tex]\ln{e^{-0.000121t}} = \ln{0.15}[/tex]
[tex]-0.000121t = \ln{0.15}[/tex]
[tex]t = -\frac{\ln{0.15}}{0.000121}[/tex]
[tex]t = 15679[/tex]
The painting is 15,679 years old.
A similar problem is given at https://brainly.com/question/16725555
