Radiometric Dating/Example/Radium in Lead/1000 Years

Example of Radiometric Dating
Let $Q$ be a sample of lead.

Let it be established that $10 \%$ of the radium decays in $200$ years.

After $1000$ years, there will be approximately $59.05 \%$ of the original amount of radium in $Q$.

Proof
From First-Order Reaction, we have:


 * $x = x_0 e^{-k t}$

where:
 * $x$ is the quantity of radium at time $t$
 * $x_0$ is the quantity of radium at time $t = 0$
 * $k$ is a positive number.

We are given that when $t = 200$, $x = 0.9 \times x_0$.

Hence:

So after $1000$ years, we have: