Question

Prehistoric cave paintings were discovered in a cave in France. The paint contained 10 %10% of the original​ carbon-14. Use the exponential decay model for​ carbon-14, Upper A equals Upper A 0 e Superscript negative 0.000121 t=A0e−0.000121t​, to estimate the age of the paintings.

Answer 1

Answer:

t=19188.2 y

Step-by-step explanation:

The exponential decay equation is:

$A=A_{0}e^{-0.00012t}$      (1)

But, A is 10% of A₀, it means that A=0.10A₀.

If we put it into equation (1), we will have:

$0.10A_{0}=A_{0}e^{-0.00012t}$      

$0.10=e^{-0.00012t}$         (2)

Now, we just need to solve (2) for t.

$t=\frac{ln(0.10)}{-0.000121} = 19188.2 y$      

I hope it helps you!