First-Order Reaction/Proof 2

Proof
From Differential Equation governing First-Order Reaction, the differential equation governing this reaction is given by:


 * $-\dfrac {\d x} {\d t} = k x$

for $k \in \R_{>0}$.

This is an instance of the Decay Equation, and has the solution:
 * $x = x_0 e^{-k t}$

Also see

 * Half-Life of Radioactive Substance