Answer: The amount of carbon-14 remaining after a certain amount of time can be modeled by the exponential decay function:
N(t) = N0 * e^(-kt)
where N0 is the initial amount of carbon-14, k is the decay constant, and t is the time elapsed since the death of the organism.
We know that the half-life of carbon-14 is 5730 years. This means that the amount of carbon-14 remaining after one half-life is:
N(5730) = 0.5N0
Solving for the decay constant k, we get:
0.5N0 = N0 * e^(-k * 5730)
0.5 = e^(-k * 5730)
ln(0.5) = -k * 5730
k = ln(2) / 5730
Now, we can use the fact that the skeleton has 20% of its original carbon-14 remaining to solve for the time since death. Let T be the time elapsed since death. Then, we have:
N(T) = 0.2N0 = N0 * e^(-k * T)
Solving for T, we get:
T = -ln(0.2) / k
Plugging in the value of k, we get:
T = -ln(0.2) / (ln(2) / 5730) ≈ 17089 years
Therefore, the human died approximately 17089 years ago.
Explanation: