Question

Prehistoric cave paintings were discovered in a cave in France. The paint contained

17% of the original carbon-14. Use the exponential decay model for carbon-14,
A=Age-0.000121t
to estimate the age of the paintings?

Answer 1

First, we need to find the decay constant, k. Since the half-life of carbon-14 is 5,700 years, we can use the formula:

k = ln(1/2) / 5700

k = -0.000121

Now we can use the formula for exponential decay to find the age of the paintings:

0.17 = e^(-0.000121t)

ln(0.17) = -0.000121t

t = ln(0.17) / (-0.000121)

t ≈ 22,000 years

Therefore, the age of the paintings is approximately 22,000 years.