# Carbon dating exponential

This means that given a statistically large sample of carbon 14, we know that if we sit it in a box, go away, and come back in 5730 years, half of it will still be carbon 14, and the other half will have decayed.

How am I supposed to figure out what the decay constant is?

In equation form we have $\dfrac=ky.$ If we multiply both sides by $$dt$$ and integrate, we get $\int \dfrac = k dt$ or $\ln y = kt C_0.$ Exponentiating both sides to get rid of the $$\ln$$ function gives $y = e^ = e^ e^.$ Then $y = Ce^$ where $$C$$ and $$k$$ are constants.

\] To keep things compact we are still writing $$k$$ instead of -0.000121.

Now divide by $$C$$: $0.09 = e^.$ Take ln of both sides at divide by $$k$$ to get $t =\dfrac = \dfrac = 19,905.$ So the skull is about 20,000 years old.

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