We all know that the interpretation of coefficients in a semilogarithmic model are approximate only. So if we find, let's say a coefficient on the independent variable X of 0.33, it is only approximately true that a one unit increase in X increases Y by 33%.

A) What would be the exact increase in Y? Explain using math and English.

B) What would be the exact increase in Y, if the model was fully logarithmic, with Y being preceded by a log function as well?