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wondering why all photos being shot have a lot of noise in the

darker, shadow area and transition areas from midtone to shadows-

very grainy, what am I doing wrong?

The noise in the background looks like reflections of light off the folds in your backdrop. Add tie strings to pull the folds out to the sides to get a flat smooth area behind your model.

I wish you had said where you think the grainy transitions are. The picture is so sharp you clearly see the texture in the cloth in the sweatshirt. But this isn't grain.

The lighting is nice and you have done a good job of capturing the character of a girl who wants to be known for her intelligence.