In one model of the changing population P(t) of a community, it is assumed that

dP/dt = dB/dt – dD/dt,

where dB/dt and dDydt are the birth and death rates, respectively.

(a) Solve for P(t) if dB/dt = k₁P and dD/dt = k₂P.

(b) Analyze the cases k₁ > k₂, k₁ = k₂, and k₁ < k₂.