Step 1 :The problem is asking for a function that models the decay of carbon-14 over time. This is a classic example of exponential decay, which can be modeled by the function \(C(t) = C_0 * (1/2)^(t/h)\), where \(C_0\) is the initial amount of carbon-14, \(t\) is the time in years, and \(h\) is the half-life of carbon-14.
Step 2 :In this case, the half-life is given as 5730 years, so the function becomes \(C(t) = C_0 * (1/2)^(t/5730)\). This function will give the fraction of carbon-14 remaining after \(t\) years.
Step 3 :Final Answer: The function that models the fraction of carbon-14 remaining in a sample after \(t\) years is \(\boxed{C(t) = C_0 * (1/2)^\frac{t}{5730}}\).