The mathematical formulas are required to calculate the population-based problems that are considered the most effective phenomenon in the present time.  Mathematics models are the logistic model and it can include the factors which can show the growth rate of the population. The high-quality mathematical data can show the number of the population in the historical years as well. The impact of the growth of the city depends on the mathematical model of the population. 

Overview of results on population 

Population is the mathematical factor where birth and death date are often considered as parameters. The static equation used to detect the population change is

[dN/dt = (b + i) – (d + e)]

Here dN defines the “change in population size” over the time period of “dt’ . However in most of the cases emigration and immigration has nominal effects on the change in population size. 

[dN/dt = b – d]

The above-mentioned state is called an equilibrium state where no fluctuation rate is found in any population size. Usually, finite, infinite, existent and hypothetical are the four types of population considered while obtaining the result from population-related mathematical problems. In most cases mean, median, mode, probability and statistics are used as effective methodology. 

Formula that are used in population-based problem 

There are many mathematical formulas that can be used to solve population-based problems. The basic formula for calculating the population of any country has been drawn below, 

Let, the population of a city is P, the increasing rate of the population is R% per annual growth, and the year has been considered as y. 

Now, (a) population after y years, P (1+R/100)y

And (b) population before y years, P/(1+R/100)y 

 Examples of population-based problem 

Population-based problems have been considered as an ever-growing phenomenon in today’s world. Every year the number of the population is increasing day by day and mathematicians use percentages to calculate the formula. For example 

1. The population of WBincreases at a rate of 9% per year but due to migration from different countries, there is a further increase in it by 1%. This 1% rate has increased in the population which needs to be calculated after the 9% increases and not on the population of previous years. Identify the amount of the increasing percentage of the population after 3 years?

Answer: 

Suppose, the population of the previous year was 100.

Now, with the 9% of increase population

The new population is, (100+9)= 109

The increasing rate of the population is 1% 

So, the 1% rate of 109 is 1.09

Now, the population will be, (109+1.09)= 110.09

The important factor in this calculation, the 9% and the 1% need to be taken separately. 

One cannot take 10% of the increasing rate in the population, 

So, the increasing rate of population after one will be 110 instead of 110.09.

For the second year, the increasing rate of the population is 9% and the population will be 9% of 110.09. The percentage will be 9.90,=> (9.90+110.09)= 119.99

The increasing rate 119.99 by 1% of rate so the new population will be 121.18

So, the population percentage will be 21.18     

Factors that affect population-based results 

There are many factors that might influence the size of the population and growth. The influential factors are, economical growth, cost of education, societal stability, policy of the government, health and safety measures and many more. There are statistical formulas which can provide the example of influential factors which might affect the population, 

Xn is the size of the population where n is the breeding period of the population, a is reproductive potential and m is the lag value of the population. 

Reason behind declination of population result 

Population decline in the human being has been considered as the decreasing rate of the population size of the humans. Sometimes the underpopulation, black death, and collapsing of the population can be considered as the population decline as well. The main reason for the decline of the population is high death rates due to pandemics, war and many more. The population decline can be caused due to long term events of demographic trends. The three population declines are birth rate, death rate and migration of the people from one country to another country. 

 Conclusion 

The assignment has been concluded on the discussion of results on population in mathematics formulas. The mathematical model can help to measure the population rate of every year. The statistical formulas and the mathematical formulas have been described as well. An example of calculating the population rate has been attached to understand the mathematical methods in calculating population-related problems. Factors of the population-based result have been described and the cause of population decline has been illustrated. The FAQs have considered answering some questions from the result of population.