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Going from large to small, you find another type of critter on the planet: alien amoebas!

Since you're stranded on the planet and there's nothing else to do except run screaming from some of the inhabitants, you decide to study amoeba populations.

Typical animal populations grow by mommy and daddy animals making baby animals.  (Hey -- these lessons are G rated!)  Amoeba populations, on the other hand, grow by each amoeba splitting into two amoebas.

So, if each alien amoeba splits into 2 amoebas every hour, can we create a formula to describe the growth of the amoeba population?

Let's say we start with 50 amoebas...

TIME ( t )
 
POPULATION
 
start:
     t = 0
50
after 1 hour:
     t = 1
50 * 2 = 100
after 2 hours:
     t = 2
50 * 2 * 2 = 50 * 2^( 2 ) = 200
after 3 hours:
     t = 3
50 * 2 * 2 * 2 = 50 * 2^( 3 ) = 400

Look familiar?
 
after  thours:

50 * 2^( t ) ... 50 is the initial population ... 2 is the split factor ... t is the number of splits

Hey!  This is just like alien monster growth!