"Consider a population P(t) satisfying the extinction- explosion equation dP/dt=aP^2-bP, where B=aP^2 is the time rate at which births occur and D=bP...

"Consider a population P(t) satisfying the extinction- explosion equation dP/dt=aP^2-bP, where B=aP^2 is the time rate at which births occur and D=bP is the rate at which deaths occur. If the initial population is P(0)=P(knot)and B(knot)=births per month and D(knot)=deaths per month are occurring at the same time t=0, show that the threshold population is M=[D(knot)*P(knot)]/B(knot)."Use differential equations to solve this problem and also note that dP/dt=aP^2-bP=aP(P-M) where M=a/b."