Models that describe the behavior of a variable over time are called growth models. Such models are used in a variety of ?elds, such as eco- nomics, biology, botany, ecology, and demography. Growth models can take a variety of forms, both linear and nonlinear. Consider the following models, where Y is the variable whose growth we want to measure; t is time, measured chronologically; and ut is the stochastic error term.

a. Yt = β1 + β2 t + ut

b. ln Yt = β1 + β2 t + ut

c. Logistic growth model: Yt = β1 /1+β2 e-β3 t+ u

d. Gompertz growth model: Yt = β1 e^{-β2 e-β3 t}+ u_t^t

Find out the properties of these models by considering the growth of Y in relation to time.