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Question: in lab we consider the gompertz equation y r...

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In lab, we consider the Gompertz equation, y' = r y ln(K/y) and simplifications of that using the Taylor expansion for ln(y) near y = 1. Here we consider the Gompertz equation as well as the linear and quadratic approximations to the Gompertz equation obtained by retaining the constant and linear terms in the Taylor expansion for ln(y).

(a) Find the critical points of all three equations and determine their stability.

(b) Solve these three equations exactly.

(c) Find the solution to each with the initial condition y(0) = 1. How is the long-term behavior of each similar and different?

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