population question?

Question

As of 2006, England is 90.9% Caucasian and 9.1% non-Caucasian, the Caucasians have 1.55 kids per woman, and the non-Caucasians have 2.8 kids per woman. Half the population are women in both groups. The life expectancy is 75 years for both groups. The death rate is 1% of the population per year. How do I figure out what percent Caucasian England will be in 2106?

Answer 1

Assume a basis: lets say 1000 people

909 are caucacian and 91 are non

there are 454.5 caucasian women and 45.5 non

then they each have 1.55 kids for cauc and 2.8 for non

yielding:

454.5*1.55 = 704.475 new cauc
45.5*2.8 = 127.4 new non

for a total population of

704.475+909 = 1613.475 cauc
91+127.4= 218.4 non

but this is only for one life cycle of 75 years and you want 100 years. so we must increase another 25%...

or 25% of:
806.7375 cauc women
109.2 non women
still need children

so again:

806.7375*1.55*0.25=312.61078125 cauc
109.2*2.8*.25=76.44 non

for a total population of

1613.475+312.61078125=1926.08578125 cauc
218.4+76.44=294.84 non

but each year 0.1% die

so in 100 years

1926.08578125 decreases by 0.1% per year to 1742.70728954237 cauc
294.84 to 266.768916655006 and the total percentage caucasian will be

1742.70728945237/( 1742.70728954237 + 266.768916655006) = 86.724455067235% or 86.7%

Answer 2

I agree with those above. Off the top of my head, I don't see a clear, or easy way to go about this. I'm not sure its there, I just don't feel like taking the half an hour or so to figure out how to do it, or if you can.

Edit: if it were a simple seventy-five year period, and assuming everyone was zero years old in 2006, it may be able to be done. However, given that it is a hundred year period, and given that we do not have a distribution of motherhood ages (ie: the age at which women become mothers), I don't really see how to complete this after seventy five years. I mean, we could do the following for seventy-five year period, but I don't like it:


Assume that there are 90.9 caucasians, and 9.1 non-caucasianas. Assume that everyone is age zero in 2006 and lives for seventy five years. Then in 2081, the original population will be dead. But during that time, caucasians will increase to 140.895, and non will increase to 25.48, for a total population of 166.375. Thus, caucasians represent a 84.685% of the population, and non represent 15.3148%.

Given that there are 25 years remaining until 2106, assume death and birthrates are 2/3 of their normal, so 1/3 of each population will die off, leaving

93.93 caucasians and
16.986 non.

And assuming that a each had a birthrate of

cacasian: 1.0333
non: 1.8666

And assuming that the deaths affect the births, (ie: if you're dead, you do not contribute), we've got

97.057869 cacuasians, and
31.706 non, which implies

75.3766% is caucasian
24.6234% is not



But I don't like this. It is a poorly framed question. This should really be set up in such a way that it can be solved with calculus.

Edit v2.0

I also like the answer below.

Answer 3

Using the information provided, the question is not answerable.

1.) of the 90.9%, how many are 'woman' and able to have the 1.55 kids per year average?

2.) what age do we begin with that a 75 year life expectancy would have any affect?

More information would be required.

Answer 4

Assuming that there is no interbreeding... i.e., whites stay with whites non-whites stay with non-whites then all you need to do is project the population into the future then take the ratio of those.

The problem with this though is that you dont have enough information.

You MUST have the following

1. Current age distribution
2. Some information about WHEN people have children. I.e. average age for a woman to give birth.

You CAN NOT make any inferences without those two.

I COULD assume that the age distributions are the same. However when they have the children is a vital piece of information and whether i assume its the same or not i need to know it.