Question

The paintings are approximately blank years old round to the nearest integer.

Answer 1

16,249 years old

Explanation:

The exponential decay model for carbon-14 is given below:

`A=A_0e^(-0.000121t)`

The paint contained 14% of the original carbon-14.

• A=14% = 0.14

,

• Ao = 100% = 1

`\begin{gathered} 0.14=e^(-0.000121t) \\ \text{ Take the ln of both sides} \\ ln(0.14)=ln(e^(-0.000121t)) \\ ln(0.14)=-0.000121t \\ \text{ Divide both sides by -0.000121} \\ t=(ln(0.14))/(-0.000121) \\ t=16248.9 \\ t\approx16,249 \end{gathered}`

The paintings are approximately 16,249 years old.