Question 752776
Continuous exponential growth {{{A=p*e^(kt)}}} where A is amount at time t and p is the initial amount for t=0.


Doubles every 30 minutes ---- let us use time units in minutes.  
{{{2p=p*e^(k*30)}}} and we want to have a value found for k.


Divide both sides by p.
{{{2=e^(k*30)}}}
{{{ln(2)=30k*ln(e)}}}
{{{ln(2)=30k}}}
{{{k=(1/30)*ln(2)}}}
{{{highlight(k=0.023)}}}


The growth model for this example is {{{highlight(A=p*e^(0.023t))}}}.
t is time in minutes
p is initial population for t=0
A is population at some time t