how do i find the equation

Question

you start with 2 bunnies. after 1 month each pair of bunnies has 6 new bunnies. how many bunnies will you have after 1 year? find the equation

Answer 1

Jennifer,

 

Here's how you do the bunny math.

 

First, assume that no bunnies die in that 1 year period.  The initial bunny pair is a breeding one, and each 6 bunnies that result from a breeding pair is 3 more breeding pairs ready to reproduce in the following month.  Then

 

Let N_o  = 2 bunnies, the starting breeding pair.

     N_n   = # of bunnies after month n for n =1,2 ...12

 

Notice that N₁ = 2 (the parent pair No) + 6 offspring = 8   (forming 4 breeding pairs)

                N₂ = 8 (parents) + (4 breeding pairs)( 6) = 8 + 24 = 32

                N₃ = 32 (parents) + (16 breeding pairs)( 6) = 32 + 96 = 128

So notice the pattern:  N_n/N_(n-1) = 4 = constant for each adjacent n's

 

Thus,  N_n = N_o (4)^{(n-1)  , (a geometric series with r =4)}

         N₁₂ = 2 (4)¹¹ =  8,388,608 bunnies after 12 months