A certain population is believed to satisfy the logistic recursion relation 1- 1

Question

A certain population is believed to satisfy the logistic recursion relation

1- 17.808

2- 43.7638011

3- 98.4637205

4- 178.444839

5- 209.216097

6- 193.79085

7- 203.417061

8- 197.856353

9- 201.249427

10- 199.237855

11- 200.45264

n Pn
A certain population is believed to satisfy the logistic recursion relation Pn+l = f(Pn) = A middot P2n + B middot Pn The data for this population can be found below. Find the constants A and B that fit the data to the update function f as well as possible in a least squares sense and use the values of A and B to predict the equilibrium values of P.

Explanation / Answer

A = - 0.008

B = 2.6

f(Pn) = -0.008*(Pn)^2 + 2.6*(Pn)

differentiate f(Pn) with respect to Pn and equate to '0' for equilibrium

Hence equilibrium value of Pn = 162.5

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