First-Order Reaction/Proof 1

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

At time $t = 0$ we have that $x = x_0$.

So:
 * $x_0 = e^c e^0 = e^c$

and hence the result
 * $x = x_0 e^{-k t}$