Hold a refrigerator magnet next to the surface of the tub. Try to stick it onto the tub. If it sticks, the tub is made of steel, as steel is magnetic. If it does not stick, the tub is made of fiberglass, which is not magnetic.
Knock on the tub three or four times and listen to the sound. If it sounds hollow, it is made of steel; if it sounds dense, it is made of fiberglass
Observe the tub for any chips or deep scratches. If you find one, investigate the material you can see through the damage. If it is black and flat, the tub is made of steel. If the material is fibrous, it is made of fiberglass.