Show That for the Following Regression Model
Y_t = ${ } _ { e } \beta _ { 0 } + \beta _ { 1 \times t + u }$

Essay

Show that for the following regression model
Y_t = ${ } _ { e } \beta _ { 0 } + \beta _ { 1 \times t + u }$ where t is a time trend, which takes on the values 1, 2, …,T, β₁ represents the instantaneous ("continuous compounding")growth rate. Show how this rate is related to the proportionate rate of growth, which is calculated from the relationship
Y_t = Y₀ × (1 + g)^t
when time is measured in discrete intervals.