Does the growth and development of a cell affect its rate of mitotic division?
Cell growth is due to the addition of more cells. Cell development involves changes to that cell.
The statement in your question is backwards. The growth and development of a cell does not affect its rate of mitotic division. Rather, the a cell's rate of mitotic division affects the cell's growth.
Mitosis (referred to as mitotic division within the question) is a form of asexual cellular division that produces more somatic (body) cells (as opposed to meiosis, which is a form of cellular division that creates additional sex cells). Prior to mitosis, replication of the genetic material within a nucleus occurs. Thus, once the parent cell divides, each of the two resulting daughter cells will receive the characteristic number of chromosomes for that species.
Within our bodies, the different types of cells undergo mitosis at different rates. Cells that undergo constant friction, such as skin and the internal lining of the intestine, must be replaced quickly via mitotic division. Skin cells are constantly dividing and the intestinal lining is replaced approximately every 2-7 days. Nerve cells, on the other hand, take a much longer period of time to undergo mitotic division.
Cells have internal and external regulators that help to control the rate of cell division. Cancer cells do not respond to the regulator called cyclin. This results in uncontrollable cell growth and tumors.