### Determine qualitatively different regimes of growth

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Find the three qualitatively different regimes of growth from the given data.

Human populations are sometimes modeled by the Gompertz equation dy/dt = ryln( k/y ) , where r and k are positive constants. If y(0) = y0 > 0 , formulate the initial value problem in terms of the dimensionless variables T = rt, and Y=y/y0. Use this formulation to distinguish and describe three qualitatively different regimes of growth

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