For the family of transformations τ(r,b,x)=rxe^-bx which models the Poincaré sections of the Belousov-Zhabotinski reaction we prove that there is an uncountable set A such that for each τξA,τ(r,b,˙) has an absolutely continuous invariant measure. We also approximate the density of this measure and thereby the Lyapunov exponent of τ(r,b,˙) .This is accomplished by proving that τ(r,b,˙) is conjugate, via an absolutely continuous homeomorphism, to a transormation T, where T^x is piecewise expanding, for some integers