A population of fish in a controlled pond is represented by a growth logistic model: Given the equation is: Pn+1 = 1.6P - 0.0003P,² where P, is the population at n-month. a) Find the value of rand M. Interpret your answers. (Hint: Hint: Pn+1 = P + rP (1-1 = P₁ + rP₂ ( 1 - where M is the carrying capacity) b) Given the initial fish population is 200. Find the population of the fish at P₁, P2, and P3. c) Sketch the solution of this model. What will happen to the population after a long time t. d) Find the equilibrium points of the given model and determine the solution's behaviour near the equilibrium points.

A colony of 120 wood frogs was introduced to a pond with a carrying capacity of  C=300. The population grows according to the logistic growth model, with a growth parameter is r = 1.5. The logistic growth formula is:  pN+1 = rpN(1-pN)   a)     Find the initial p-value:   p0  = Answer   b)     Find the first p-value: p1 = Answer   c)     Find the second p-value:  p2  = Answer

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 =   After two breeding seasons the population of the pond is given by�2 =

The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?