Question

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

Answer 1

Answer:

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

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

The paintings are approximately 16,249 years old.