Carbon-14 is a radioactive isotope used to determine the age of samples of organic matter. The amount of carbon-14 in a sample decreases once the organism is no longer alive. The half-life of carbon-14 is approximately 5730 years. This means that every 5730 years, the amount of carbon- 14 in an organism that is no longer living will be halved. Which of the following functions, $C$, bmodels the fraction of carbon-14 remaining in a sample after $t$ years?

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 \(\boxed{C(t) = C_0 * (1/2)^\frac{t}{5730}}\).