It is determined that the charcoal in a fire pit used as an ancient hearth has lost about 42.3% of the initial ¹⁴C. How old was the fire pit if ¹⁴C has a half life of 5730 years?

Question

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The amount of ¹⁴C remaining after t years is given by the equation:```N(t) = N(0) * (1/2)^(t/t1/2)```where:* N(t) is the amount of ¹⁴C remaining after t years* N(0) is the initial amount of ¹⁴C* t1/2 is the half-life of ¹⁴CIn this case, we know that N(t) = 0.577 * N(0), since the charcoal has lost about 42.3% of the initial ¹⁴C. We also know that t1/2 = 5730 years. Substituting these values into the equation, we get:```0.577 * N(0) = N(0) * (1/2)^(t/5730)```Solving for t, we get:```t = 5730 * log(2) / log(0.577) = 4550 years```Therefore, the fire pit is 4550 years old.

It Is Determined That the Charcoal in a Fire Pit