Table 1. Functional forms of growth models.

Growth Model	Functional form: f(t)	Parameters with expected signs
Cubic	α + β * t + γ * t2 + θ * t3	α, β, γ, θ
Exponential	M + α * exp[−β * t]	M, α, β
Logistic	$\frac{\mathrm{M}}{1+\mathrm{\alpha }\ast exp[-\mathrm{\beta }\ast \mathrm{t}]}$	M, α, β (M > 0, β > 0)
Log-logistic	$\frac{\mathrm{M}}{1+\mathrm{\alpha }\ast exp[-\mathrm{\beta }\ast log(\mathrm{t})]}$	M, α, β (M > 0, β > 0)
Weibull	M − α * exp(−β * tγ)	M, α, β,γ (M > 0, β > 0)
Gompertz	M * exp[−α * exp(−β * t)]	M, α, β (M > 0, β > 0)
H1	$\frac{\mathrm{M}}{1+\mathrm{\alpha }\ast exp[-\mathrm{\beta }\ast \mathrm{t}-\gamma \ast arcsin\mathrm{h}(\mathrm{t})]}$	M, α, β, γ (M > 0, β > 0)
H2	$\frac{\mathrm{M}}{1+\mathrm{\alpha }\ast arcsin\mathrm{h}[exp(-\mathrm{\beta }\ast {\mathrm{t}}^{\gamma })]}$	M, α, β,γ (M > 0, β >0)
H3	M−α * exp[−β * tγ − arcsinh(θ * t)]	M, α, β, γ,θ (M>0, β >0)

Recall that $arcsin\mathrm{h}t=ln(t+\sqrt{t^2+1})$ is the inverse hyperbolic sine function of t.