solve it by using matlab and explain how this application would be related to industrial engineering

PART 2a (30+10 points) - Population Growth Modelling (30 points) For a given population we are trying to get a model for the growth. For that we need to consider several factors. Here in the current task, we will focus on fertility, initial number of members in population and death rate. Here let ni(t) to represent the number of individuals of age i in year t,pi to represent the probability (proportion) of an individual to live from year i to next year i+1, and fi to represent the fertility rate of individuals at age i. Then we can relate all these terms by following formulas ni+1(t+1)=ni(t)pi,fori>1,i=1Tfini(t)=n1(t+1). Please be sure that these relations are clear. Now let m(t) represents the column vector of whole population at year t where each row represents the population of a certain age. In other words m(t)=[n1(t);n2(t);.nT(t)], where T is the age of the oldest individual in the population. We can relate m(t) with m(t+1) by a model by matrix multiplication. Find that model. (you need to find matrix L where m(t+1)=Lm(t).) (10 points) Please explain how this application would be related to your major department