Question

Prehistoric cave paintings were discovered in a cave in France. The paint contained 3% of the original carbon-14. Use the exponential decay model for carbon-14, A=A0e^-0.000121t, to estimate the age of the paintings.

The painting area approximately __ years old.

Answer 1

The painting area is approximately 28980 years old.

Explanation:

The model for the amount of carbon-14 after t years is given by:

`A(t) = A(0)e^(-0.000121t)`

In which A(0) is the original amount.

The paint contained 3% of the original carbon-14.

This means that
`A(t) = 0.03A(0)`. This means that we have to find t.

`A(t) = A(0)e^(-0.000121t)`

`0.03A(0) = A(0)e^(-0.000121t)`

`e^(-0.000121t) = 0.03`

`\ln{e^(-0.000121t)} = ln(0.03)`

`-0.000121t = ln(0.03)`

`t = -(ln(0.03))/(0.000121)`

`t = 28980`

The painting area is approximately 28980 years old.