5. Another equation that has been used to model population growth is the Gompertz equation dP...

5. Another equation that has been used to model population growth is the Gompertz equation dP /dt = rP ln (K P ) , where r and K are positive constants, and P(t) > 0.

(a) Sketch a clearly labeled graph of f(P), where dP/dt = f(P) (state the main facts you used to obtain your answer).

(b) Draw the phaseline. Next to it, sketch a set of integral curves in the t − P plane.

(c) State and classify all equilibria.

(d) (Extra Credit) For 0 < P < K, find P 00(t) and determine where the graph of P(t) is concave up and where it is concave down. Enter the inflection point in your graph in (a). (Enter your answer in an attached blank page.)

Expert Solution

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Colby Messinger answered 2 years ago

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