Suppose that the fraction of chicks that survive, P(N), as a function of the number N of eggs laid, is given by the following forms (variants of the model studied in Example 2.5.14). The total number of offspring that survive is S(N) = N ∙ P(N). Find the number of surviving offspring when the bird lays 1, 5, or 10 eggs. Find S'(N). Sketch a graph of S(N). What do you think is the best strategy for each bird?
P(N) = 1 / 1 + 0.1N2.