Auxin probably first binds to a receptor molecule and this complex then actives the pump. ATP stimulated acidification is observed very quickly after auxin treatment. Auxin stimulates transcription and translation. The proton effect is short-lived. Cell elongation stops 30-60 minutes after acidification.
Continuous elongation requires longer term metabolic changes such as protein synthesis.
C. Wall synthesis occurs . As the cell grows cell wall synthesis will need to occur. As an example, think about the color of a balloon as it is blown up - it gets lighter in color as the balloon gets larger because the thickness of the balloon decreases as it expands and stretches. Using this logic, we expect that plant cells should become thinner as they expand. Wrong - cell walls remain a relatively uniform thickness throughout cell growth.