Solving the Rate Equation

Consider the following reaction:

$\mathrm{B} \rightarrow \mathrm{X}$

The reaction is first order in B, and has the rate equation,

$\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{d}t} = -k\left[\mathrm{B}\right]\,$

where $k$ is the rate constant.

Equations of this type occur frequently in science. We obtain the solution by firstly dividing by $\left[\mathrm{B}\right]$.