1. The Gompertz differential equation

dy

dt

y (a-blny),

where y> 0 and a and b are parameters, is used in actuarial studies, and to model growth of objects as diverse as tumors and

organizations.

(a) Find all equilibrium solutions.

(b) Use the substitution z = In y to find the general solution of the Gompertz differential equation.

(c) Solve the IVP consisting of the Gompertz differential equation and the initial condition y(0) = yo > 0.

(d) Describe the limiting value for y(t) as too. Assume that a > 0, and consider the cases b>0 and b < 0.