Rewrite variable in given constants and variables

Hello everyone,

English isn't my native language, so I hope I can make myself clear. I'm new on this forum, because I have a question. I put this topic in this subforum, but I am not sure if this is the right one. Sorry if I'm wrong.

Given is some vector and with following conditions:

with

In this case: . and are constants.

with and with are constants too.

Let be a vector with above mentioned conditions ánd:

Define . Express in , and .

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I have a very difficult time doing this. This is how far I got:

.

So for :

.

I think I have to substitute somewhere in in a way that only , and remain as constants/variables.

Later I found that:

And for :

.

But I don't know what I can do with that.

---

Anyone who can help me with this?

Thanks in advance.

Re: Rewrite variable in given constants and variables

Hey Fruitbowl.

Can you outline broadly what you are trying to do? (What is the goal of your problem in non-mathematical terms)?

Re: Rewrite variable in given constants and variables

This task is about demography and making mathematical models. (and ) stands for the amount of people in age group at time . There are age groups labeled to . For example, in age group 0 the people are between 0 and 9 years old, in age group 1 between 10 and 19, etc.

is the probability of survival for people in age group . So the amount of people is equal to the amount of people multiplied by the probablity of survival . Hence,

This is different for the amount of people , because there are no things like and . So this is a special case. is the fertility factor of the people in age group . is between and , where , because people stop 'producing' children when they get past a certain age.

So the amount of people .

I hope this makes it more clear.

**Edit:**

And B is a stationary population in this case. So . So the proportion between and is always the same at a certain time and for all

Re: Rewrite variable in given constants and variables

< I'm sorry I posted above mentioned message twice >

Re: Rewrite variable in given constants and variables

I'm still a little lost: What exactly are you trying to answer? Do you want to find average survival? Maybe find some kind of optimal survival attribute? Maybe use this to design insurance premiums (like life insurance contracts)?

Re: Rewrite variable in given constants and variables

Later in this task I have to show that every population will converge to a stationary population (in this case ).

The thing I have to do here is to express in , and .