An exponentially increasing function, in the constant-rate exponential growth model, has the form
 |
where 
and 
are constants. Its derivative satisfies 
(Strang and Herman 2016). The prototypical example
is the exponential function 
, plotted above.
Growth faster than every polynomial does not by itself imply exponential growth. For example, 
grows faster than 
for every fixed 
as 
,
but more slowly than 
for every fixed 
.
