First-Order Reaction

Theorem
Let a substance decompose spontaneously in a first-order reaction.

Let $x_0$ be a measure of the quantity of that substance at time $t = 0$.

Let the quantity of the substance that remains after time $t$ be $x$.

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

where $k$ is the rate constant.

Also see

 * Half-Life of Radioactive Substance