recurrence relation number of bacteria Assume that growth in a bacterial population has the following properties:


*

*At the beginning of every hour, two new bacteria are formed for each bacteria that lived in the previous hour.


*During the hour, all bacteria that have lived for two hours die.

*At the beginning of the first hour, the population consists of 100
    bacteria. 


Derive a recurrence relation for the number of bacteria.
I know that if the bacteria wouldn't die $A_{n} = 2A_{n - 1}$, but now I have no idea what to do.

We know $A_1 = 100$, and in the second hour there will be $200$ newborn and $100$ that will die the third hour. So, $A_2 = 300$. Those $300$ alive in the second hour mean that in the third hour there will be $600$ newborn and $200$ still alive; $A_3 = 800$.
Following this logic, we can define: 
$$A_n = 2 \, A_{n-1} + 2 \, A_{n-2}.$$
