1. Suppose that a population grows according to the 'logistic model' and is harvested at a rate

proportional to the size of the population. The dynamics of the density x(t) of the

population is governed by

x = kx-cx²-hx,

where all the coefficients are positive; k and c reflect the growth rate of the population and

h is the rate of harvesting. The problem is to determine the effect of harvesting on the

population, given values of constants k and c.

(a) show that if k 0, such a population tends

toward extermination as t->∞, but is not exterminated in finite time.

(b) also, analyze the fate of the population in the cases k = h and k> h.