# Thread: Differential Equation -- Half Life Decay Question

1. ## Differential Equation -- Half Life Decay Question

The so-called "Pittsburgh man" unearthed near the town of Arella, Pennsylvania, shows that civilization existed there from around 12,300 BC to 13,000 BC. Calculate the difference between the percentage of C14 lost prior to 2000 AD from a bone of someone who died in 12,300 BC and that from someone who dies in 13,000 BC.

2. ## Re: Differential Equation -- Half Life Decay Question

Let c(t) be the level of C14 at time t. Then $\displaystyle c(t)=c_0e^{-kt}$ where $\displaystyle c_0$ is the level at t = 0 and k is some constant.

(1) Find k from the fact that $\displaystyle c(5730) = c_0/2$ (5,730 years is the half-life of carbon-14).
(2) Find $\displaystyle \frac{c(0) - c(14300)}{c(0)}$, which is the percentage of C14 lost between 12300BC and 2000AD.
(3) Find $\displaystyle \frac{c(0) - c(15000)}{c(0)}$, which is the percentage of C14 lost between 13000BC and 2000AD.
(4) Find the difference between (3) and (2).