Consider the chemical reaction in which two monomers of A combine to form a dimer $B,$ according to

$A+A>{?}^{k}B$

where the forward rate is $k_{+}$and the backward rate is $k_{-}.$

a$.$ Use the law of mass action to find the differential equations governing the rates of production of A and $B.$

b$.$ Notice that every $B$ represents $2A($or two monomers of $A).$ Therefore, if the initial amount of $A$ is $A_0,$ then $a+2b=A_0$ where $a=[A]$ and $b=[B].$ Use this conservation relationship to find an equation for $\frac{da}{dt}$ that depends only on $a.$