Question

Log-lin model in simple regression:

y_i=B₀.B₁^X_i.e^u_i   $\rightarrow$ take natural log of both sides $\rightarrow$ lny_i=lnB₀ + (lnB₁)x_i + u_i . Take lny_i = w_i, lnB₀= B^*₀ and lnB₁=B^*₁ so the former equation equals to w_i= B^*₀ + B^*₁ + u_i. It is said that, when you increase x by 1 unit, you expect B^*₁ % change in y.

B^*₁ $= \frac{dlnyi}{dxi}$ =(dy_i/y_i​) / dx_i = $= \frac{\Delta yi/yi}{\Delta xi}$ = (((y_i-y_i-1)/y_i) / (x_i- x_i-1))*100 . question is about the numerator, (y_i-y_i-1)/y_i)*100:

1)It is said that the numerator reflects the percentage change in y, then why it is not ((y_i-y_i-1)/y_i-1) but instead ((y_i-y_i-1)/y_i) ? Why don't we divide by y_i-1 (the value before i-th term,or the past value) instead of y_i (the i-th term, or the current value) ?

2) Does ((y_i-y_i-1)/y_i)*100 really stand for the percentage change in y?