Question: The Gompertz equation dy/dt = y(a-b ln y) where a and b are parameters, is used in actuarial studies, and to model growth of objects

The Gompertz equation dy/dt = y(a-b ln y) where a and b are parameters, is used in actuarial studies, and to model growth of objects as diverse as tumors and organizations.
(a) Show that the solution to the Gompertz equation is y(t) = ea/bece-bt
(b) Solve the IVP for this equation with y(0) = y0.
(c) Describe the limiting value for y(t) as t → ∞.
Assume that a > 0, and consider the cases b > 0 and b < 0.

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a Letting z ln y and using the chain rule we get Hence the Gompe... View full answer

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