5. Another equation that has been used to model populationgrowth is the Gompertz equation dP /dt = rP ln (K P ) , where r andK 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 integralcurves in the t ? P plane.
(c) State and classify all equilibria.
(d) (Extra Credit) For 0 < P < K, find P 00(t) anddetermine where the graph of P(t) is concave up and where it isconcave down. Enter the inflection point in your graph in (a).(Enter your answer in an attached blank page.)
