Given the population in 2017,$P_0=80$ Million and birth at the same year was $B=700.000$, whereas the death rate the same year was $D=900.000.$ I need to predict the population in 50 years by assuming the logistic equation $$\frac {dP}{dt}=\mu (1-\frac{P}{K})P - D P$$. I got the solution of the differential equation being $P(t)=\frac{\mu -D}{\frac{\mu}{K}-exp(-(\mu -D)t)},$ where $\mu$ is the growth rate,$K$ is the capacity. It was assumed that birth rate, death rate and population growth is proportional to the total population.
I got the result $P(50)=0, $which I dont understand. I might have done a mistake. Can somebody point me out what I did wrong ?
Many thanks.