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Log-lin model in simple regression: yi=B0.B1Xi.eui   take natural log of both sides lnyi=lnB0 + (lnB1)xi +...

Log-lin model in simple regression:

yi=B0.B1Xi.eui  \rightarrow take natural log of both sides \rightarrow lnyi=lnB0 + (lnB1)xi + ui . Take lnyi = wi, lnB0= B*0 and lnB1=B*1 so the former equation equals to wi= B*0 + B*1 + ui. It is said that, when you increase x by 1 unit, you expect B*1 % change in y.

B*1= \frac{dlnyi}{dxi} =(dyi/yi​) / dxi = = \frac{\Delta yi/yi}{\Delta xi} = (((yi-yi-1)/yi) / (xi- xi-1))*100 . question is about the numerator, (yi-yi-1)/yi)*100:

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

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

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