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

t=19188.2 y

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=(ln(0.10))/(-0.000121) = 19188.2 y`

I hope it helps you!