Question

Find the age of the mammal hide to the nearest year. A farmer in China discovers a mammal hide that contains 71% of its original amount of C-14. The decay formula is given by N = Noe^(-kt), where N is the amount at time t, No is the initial amount of C-14 (at time t = 0), k is the decay constant (given as 0.0001), and t is time in years.

What is the value of root 2 * root 6?
A) root 3
B) 3 root 2/4
C) root 3/2
D) root 2/2

Answer 1

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.