Final answer:
To calculate the age of the mammal hide, we use Carbon-14 dating with the decay formula and the given percentage of C-14 remaining. The decay constant is derived from the half-life of C-14, and the age is then calculated by solving for t.
Step-by-step explanation:
To find the age of the mammal hide, we utilize the decay formula N = Noe-kt, where N is the current amount of C-14, No is the original amount of C-14, k is the decay constant, and t is the time in years. Given that the mammal hide contains 71% of its original C-14, we set N/No to 0.71.
The decay constant k can be found from the known half-life of C-14, which is 5730 years, using the equation k = 0.693 / t1/2. Substituting the given values, we get k = 0.693 / 5730 = 0.0001.
The age can be calculated by rearranging the decay equation to solve for t: ln(N/No) = -kt, thus t = -ln(N/No) / k. Plugging the values in, we get t = -ln(0.71) / 0.0001. After calculating, we can approximate the age of the hide to the nearest year.
Carbon-14 dating is generally used to determine the age of biological materials that are not older than about 50,000 years, making it an essential tool in archaeology and paleontology.