.
Thus, one can say that grows much faster than as increases.
To make these ideas more precise, we have the following:
Let We say that
grows slower than as if
Then Thus, grow at the same rate as .
. 
grows much faster than 
as 
increases.
We say that 
grow at the same rate as 
if 
grows slower than 
as 
if 
grows faster than 
as 
if 
grow at the same rate as 
. 
