4.3.3 Solution of the revised equation

Solving the equation, subject to the initial condition P = P0 at t = 0 gives the result

<

Clearly, if h is chosen so that is positive, then the population will grow exponentially. If however h is chosen so that is negative, the population will die out at a time t given by , or

The permissible harvesting rates are given by the inequality h < kP0.