Gnomons, Growth Population Model Question Help!

Question

A population of guinea pigs grow according to the following transition rule: P_N = 2P_N-1 + P_N-2. The starting population is P₀ = 3 and the population in the first generation is  P₁ = 5.

 

Can the size of the guinea pig generation ever be an even number? Why?

Answer 1

Hi Christopher.

 

P₀ = 3

P₁ = 5

 

Then P₂ = 2P₁ + P₀

P₂ = 2(5) + 3 = 13

 

Notice that so far P has always been odd.

 

P will continue to be odd since the P_N-2 term will always be odd.  It will always be added to an even number (since we have 2P_N-1.  An even number plus an odd number will always be odd.  Therefore the guinea pig generation will never be even.