Final answer:
Osteoblasts are the biochemically active bone cells that increase in number when bone becomes denser, contributing to bone formation by depositing new bone material.
Step-by-step explanation:
The biochemically active bone cells that increase in number when bone becomes more dense are the osteoblasts. These cells are responsible for bone formation and they synthesize and secrete both the organic and inorganic parts of the bone matrix. Osteoblasts deposit new bone material into the matrix and as they become trapped in this matrix, they differentiate into osteocytes, which are less metabolically active. However, it's the osteoblasts' activity in producing new bone material that is crucial for increasing bone density. When bone is subjected to stress, such as during exercise, the number of osteoblasts increases to strengthen the bone.