Exponential Growth and Decay

                N(t) =  N_o  e ^kt   

General form though we could have a number where we have ‘e’.
Here the growth or decay is not linear
 ie it does not increase or decrease by the same amount each time.
The growth or decay increases or decreases by multiples of an amount 
ie if it doubles each second and you start with 3 units then after 4 seconds, it would be 48 units
The equation for this situation would be

N(t) = 3 (2) ^t   

These questions are not too difficult to solve we just need to be careful.  There are several possible questions that can be asked.

 Click to find what these letters stand for

 N(t) =  N_o   e  ^kt

When is half of the initial amount of material left?
 or
When has the population doubled?

   K is the Growth or Decay Factor

Amount Present at this time

When will the amount of material exceed this number?

   Exponential Growth Example

If a colony of ants starts with a population of 25 000 then after 10 hours there are 40 000 ants.
If the population follows an exponential growth of
  Q(t) =  Q_o e  ^kt
Find the value of k
and
when the population exceeds 60 000 ants