Demographics question?

Question

Italy has 55,226,833 Italians and 2,906,676 non-Italians, the total fertility rate is 1.15 children per woman for Italian women, and 3.84 for non-Italian women, the life expectancy is 80 years for both groups and there is 300,000 Non-Italians coming in every year, how would you calculate the precise year in which Italy would have a non-Italian majority?

If I am missing anything can you tell me and work it in the problem?

Answer 1

Elementary growth of aboriginal population in time dt: dy=y*h*dt, where h is annual rate of growth, hence y=y0*exp(ht), where y0=55226833 is aboriginal population today; here I assume h = (1.15/2-1)/80 = -0.0053125 persons / year;
Elementary growth of immigrant population in time dt: dz=z*g*dt+v*dt, where g is annual rate of growth, v=300000 is annual immigration rate, hence z = (z0+v/g) * exp(gt) – v/g, where z0=2906676 is immigrant population today; ; here I assume g = (3.84/2-1)/80 = 0.0115 persons / year;
The equation for the verge time is y(t)=z(t) or t = 70 years. A duce in Roma or Brussels may come sooner.

Answer 2

You have not given the age wise distribution of Italian and non italian communities in the current population. Say what percentage of population is in the range of 75-80 years, how many of them in tha range of 70 - 75 years etc ..... 0-5 years.

Without this it is not possible to find the solution. Say, if the whole population if in the range of 75 - 80 years old, then no one would remain from the existing population in near future.

Answer 3

you also have to tell us how many italian vertil women and how many non-itialian vertil woman. This you have to tell us for each year.