What is the difference between these two methods of FGM modeling?

I want to model a FG solid cylinder with exponential profile.

In most papers, models such as Voight, Mori-Tanka, Halpin-Tsai and … are used to model functionally graded materials, and exponential function and power function are used to determine the volume fraction.

E=E1V1+E2V2     &      V1+V2=1

V1=Arn

Where E, V and r are respectively, the modulus of elasticity, volume fraction and the radial coordinate.

But in some other papers, the material properties are modeled using exponential function alone, and models like Voight are not used at all.

E=E0*exp(-n(r/b)k)

Where E0 is a reference value of E and b is the radius.

What is the difference between these two methods of FGM modeling?

I can model the FG solid cylinder with exponential profile, using the second method. But I can’t use the first method, because the Ln function is not defined at zero.