Re: What causes the cells to divide quicker at a younger age?

The cells necessarily do not divide faster at a younger age but rather the
ability to divide reduces 
with age and hence the growth rate slows down.  Cells isolated from a sample
tissue termed 
“primary cells” can divide in culture for roughly 30 divisions after which the
cells stop growing.  
This limit has been called the “Hayflick Limit” after the person who first
described the 
phenomenon. However, mutations or changes in proteins that control cell cycle
checkpoints 
during cell division leads to transformed or immortalized cells. Such cells can
grow indefinitely in 
culture, a feature shared by cancer cells. 

So if your question is can we makes cells grow forever, the answer is yes but
then the cells would 
be cancerous.  A related question would be “Can the cells remain young retaining
their ability to 
divide normally without aging?”

One of the key reasons cells senesce/age is due to shortening of the ends of
chromosomes 
called telomeres.  Several human diseases that show signs of premature aging
such as Fanconi 
anemia, Bloom’s syndrome, Werner’s syndrome etc., are associated with short
telomere length.  
Enzymes called telomerase of which hTERT or Telomerase Reverse transcriptase is
important 
maintain the telomere lengths.  Based on experiments carried out in lower
organisms, it has been 
thought for a while that this gene alone can prevent organisms from aging. 
Mammalian cells 
that express high levels of TERT such as stem cells and certain kind of cancer
cells can grow in 
culture for long periods of time.  It is however unclear how much of this alone
is responsible for 
human aging.