1. Linear model

Vol = β 0 + β 1 Age + ε

2. Quadratic model

Vol = β 0 + β 1 Age + β 2 Age 2 + ε

3. Cubic model

Vol = β 0 + β 1 Age + β 2 Age 2 + β 3 Age 3 + ε

4. Linear hybrid model: Exponential cumulative distribution for growth with linear model aging

$\mathit{Vol}={\beta }_4\left(1-e^{-\mathit{Age}/{\beta }_5}\right)+{\beta }_0+{\beta }_1\mathit{Age}+\epsilon$

5. Quadratic hybrid model: Exponential cumulative distribution for growth with quadratic model aging

$\mathit{Vol}={\beta }_4\left(1-e^{-\mathit{Age}/{\beta }_5}\right)+{\beta }_0+{\beta }_1\mathit{Age}+{\beta }_2{\mathit{Age}}^2+\epsilon$

6. Cubic hybrid model: Exponential cumulative distribution for growth with cubic model aging

$\mathit{Vol}={\beta }_4\left(1-e^{-\mathit{Age}/{\beta }_5}\right)+{\beta }_0+{\beta }_1\mathit{Age}+{\beta }_2{\mathit{Age}}^2+{\beta }_3{\mathit{Age}}^3+\epsilon$