Gompertz Equation The Gompertz equationwhere a and b are parameters, is used in actuarial...

Gompertz Equation The Gompertz equation

where a and b are parameters, is used in actuarial studies, and to model growth of objects as diverse as tumors and organizations.6

(a) Show that the solution to the Gompertz equation is . HINT: Let z = ln y, and use the chain rule to get a linear equation for dz/dt.

(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.