Populations revisited | Scoins.net | DJS

Populations revisited

Rabbits

Think of maximum poppulation as one, so that the exisiting populationis a number in the interval (0,1). Next year's population is the product of three factors: r, which we'll think of as fertility;  the existing—this year's— population; the remaining capacity for population. 

Formula:  xₙ₊₁ =  xₙ (1-xₙ).

Pick a start value. Doesn't matter what. Choose a value for r under between 2 and 3. Find your iterating calculator and do your first calculation for the next population, a number between zero and unity. Then set up your calculation dso that ANS replaces xₙ. Each time you press = the calculatore repeats the calculation.  I started with r=2.3 and whatever initial population I choose the process rapidly reaches 0.565217391. So this is a balanced population, the factors that cause a population to balance are working.
Persuade a classful of students to do this and see if there is a relationship between r and the result.

See what happens with r = 3.2.  I got a weird cycling  between 0.513044510 and 0.799455490. I wonder if these two values are connected

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