Prehistoric cave paintings were discovered in a cave in France. The paint contained 3% of the original carbon-14. Use the exponential decay

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.

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Elliana 1 week 2021-10-12T13:18:29+00:00 1 Answer 0

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    2021-10-12T13:19:55+00:00

    Answer:

    The painting area is approximately 28980 years old.

    Step-by-step 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 = -\frac{\ln{0.03}}{0.000121}

    t = 28980

    The painting area is approximately 28980 years old.

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