The continuous growth rate model stipulates that the rate of population change 
is in proportion with the actual population 
(a function of time 
). That is, there is some 
such that
Solving for
, you get
You're given that
, so the population is increasing. At time 
, you start with 2 bacteria, so 
and
So, the growth equation is
Solving for
You're given that
So, the growth equation is