5. Many animals that live in a group are unable to thrive if the group size is t

Question

5. Many animals that live in a group are unable to thrive if the group size is too small. We wish to model such a population with a dynamical equation of the form xt +1 = f (xt ) .

Suppose that a certain type of grazer needs at least 20 individuals in the herd in order to effectively defend against predators. For herd sizes numbering less than 20, the population will shrink to zero. For herd sizes between 20 and 200, the population will tend towards a stable equilibrium of 100 animals. For herd sizes greater than 200, the grazers deplete the environment to such a degree that the herd size drops below the critical value of 20.

Sketch a function y = f (x) on the axes below so that the dynamical equation xt +1 = f (xt ) models this population.



The graph they gave me is just a blank graph with x scale 50 from 0-300 and y scale 50 from 0-300

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