  We provide a new method for constructing the anisotropic relaxation tensor
and proving its exponential decay property for the extended Burgers model
(abbreviated by EBM). The EBM is an important viscoelasticity model in
rheology, and used in Earth and planetary sciences. Upon having this tensor,
the EBM can be converted to a Boltzmann-type viscoelastic system of equations
(abbreviated by BVS). Historically, the relaxation tensor for the EBM is
derived by solving the constitutive equation using the Laplace transform. (We
refer to this approach by the L-method.) Since inverting the inverse Laplace
transform needs a partial fractions expansion, the L-method needs to assume
that the EBM elasticity tensors satisfy a commutivity condition. The new method
not only avoids this condition but also enables obtaining several important
properties of the relaxation tensor, including its positivity, smoothness with
respect to the time variable, its exponential decay property together with its
derivative, and its causality. Furthermore, we show that the BVS converted from
the EBM has the exponential decay property. That is, any solution for its
initial boundary value problem with homogeneous boundary data and source decays
exponentially as time tends to infinity.
