Let P(t) be the population of a city after t years. In this city the death rate is alpha times the population size, the birth rate is beta times the population size and the immigration out of city is with rate m.
(a) Write a differential equation for the population. What is the general solution?
(b) If the initial population is 1,000,000 people, the birth rate divided by the population size is .02 bigger than the death rate divided by the population size, and 100,000 people leave the city per year. What will be the population be after 2 years?
(c) Under this model and the values given in part b), will the population expand or decline?
(d) If the 100,000 people leave the city per year, then for what value of the dierence between and does the population stay constant?
Im not sure how to approach this problem.
What do they mean by the general solution?
for the differential equation im thinking that P(t) is just a function of the initial population times alpha plus the initial population times beta plus m. does that sound right?
once i get that I think i should be able to figure out the rest.
Any help is appreciated.