The Exponential Model

N(t) - Number of population at time t, which is measured in appropriate units.b(t) - Birth Rate, c(t) - Death ratea(t) = b(t) - c(t) is the Growth Rate. This gives dN/dt = aN. This is separable and solves to give solution logN = at + C (C is an arbitrary constant). If we are given an inital condition, such as N(0)=n, we can find a particular solution to the model, N=nexp(at). These solutions depend on two parameters, the growth rate a and the initial condition n.Qualitative observations;a>0 (b>c), N tends to infinity as time tends to infinityaa=0 (b=c), N=n as time tends to infinity