Problem#$6$:

Predicting growth of US population segments. Use the US population dynamics model from $9\mathrm{.}2$

of VMLS to predict the growth of the following population segments over the years $2010-2020,$

ignoring immigration and emigration, and assuming the birth and death rates remain constant.

Plot the results.

The total US population.

The total US population age $65$ and older.

The total US population age $6-18($i$.$e$.,$ school age$).$

The total US population age $19-22($i$.$e$.,$ college age$).$

$($The number ranges are inclusive, for example, $19-22$ means $19,20,21,$ and $22.)$

Hints.

For each subpopulation, find a $100-$vector $c($different for each subpopulation$)$ for which the

subpopulation is $c^{T}x,$ where $x$ gives the age distribution. Alternatively, you can use slicing

and the sum function, as in sum$($x$[$a:b$]),$ with a and $b$ suitably defined.

See $9\mathrm{.}2$ of the VMLS Julia companion for how to get the required data, code examples, and

some critical Julia hints. To simulate the population dynamics, we suggest following the code

segment given in $9\mathrm{.}1$ of the VMLS Julia companion, which would create a $10011$ matrix $x$

with columns giving the population distribution in $2010,$dots,$2020.$ Then the $11-$vector $x^{T}c$

gives the predicted subpopulation. $($You can also use slicing as mentioned above.$)$