Final answer:
The nurse should document this as a Stage IV pressure ulcer, which is the most severe stage characterized by full-thickness tissue loss and infection.
Step-by-step explanation:
The nurse should document this as a Stage IV pressure ulcer. A Stage IV pressure ulcer is the most severe stage of pressure ulcers, characterized by full-thickness tissue loss with exposed bone, tendon, or muscle. The presence of black, necrotic tissue and purulent, foul-smelling exudate indicates that the tissue has become necrotic and the wound is infected. In addition, the rapid progression of the infection and the worsening condition of the patient further confirm that this pressure ulcer is at Stage IV.