Model Exponential Growth and Decay
Solve.
-A fossilized leaf contains 18% 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)13,829
B)23,309
C)1600
D)35,538

Question

Quizplus · Accepted Answer

The age of the fossil can be determined using the formula for exponential decay, $N = N_0 \times (1/2)^{\frac{t}{T}}$, where $N$ is the remaining amount of substance, $N_0$ is the initial amount, $t$ is the time, and $T$ is the half-life. Given that $N/N_0 = 0.18$ and $T = 5600$ years, solving for $t$ gives approximately 13,829 years.