Solve the problem.
-A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.
A)1031
B)17,099
C)36,108
D)20,040

Question

Quizplus · Accepted Answer

The age of the fossil can be calculated using the formula for radioactive decay, $N = N_0 \times (\frac{1}{2})^{\frac{t}{T}}$, where $N$ is the remaining amount of substance, $N_0$ is the initial amount of substance, $t$ is the time that has passed, and $T$ is the half-life of the substance. Given that $N/N_0 = 0.12$ (or 12%) and $T = 5600$ years, we can solve for $t$. Rearranging the formula gives us $t = \frac{T \times \log(N/N_0)}{\log(1/2)}$. Plugging in the values gives us $t \approx 17,099$ years.

Solve the Problem. -A Fossilized Leaf Contains 12% of Its Normal Amount of Normal