I need some help in explaining the main formula given in the Overview section of this article.

OVERVIEW Each year, the United States Census Bureau produces and publishes estimates of the population for the nation, states, counties, state/county equivalents, and Puerto Rico.1 We estimate the resident population for each year since the most recent decennial census by using measures of population change. The resident population includes all people currently residing in the United States. With each annual release of population estimates, the Population Estimates Program revises and updates the entire time series of estimates from April 1, 2020 to July 1 of the current year, which we refer to as the vintage year. We use the term \"vintage\" to denote an entire time series created with a consistent population starting point and methodology. The release of a new vintage of estimates supersedes any previous series and incorporates the most up-to-date input data and methodological improvements. The population estimates are used for federal funding allocations, as controls for major surveys including the Current Population Survey and the American Community Survey, for community development, to aid business planning, and as denominators for statistical rates. Overall, our estimates time series from 2000 to 2010 was very accurate, even accounting for ten years of population change. The average absolute difference between the final total resident population estimates and 2010 Census counts was only about 3.1 percent across all counties? We produce estimates using a cohort-component method, which is derived from the demographic balancing equation: Population Population Births - 1- Migration Base Estimate The population estimate at any given time point starts with a population base {e.g. the last decennial census or the previous point in the time series), adds births, subtracts deaths, and adds net migration (both international and domestic}.3 The individual methods we use account for additional factors such as input data availability and the requirement that all estimates be consistent by geography and age, sex, race, and Hispanic origin. This document describes the input data, methodology, and processes for the creation of population estimates for the nation, states, counties, statefcounty equivalents, and Puerto Rico. We begin with a short discussion on consistency in the estimates, describe the input data, and detail the processes by which we produce estimates. Estimates Consistency, Controlling, and the Residual We produce the estimates using a "top-down\" approach. Given that it is generally more reliable to estimate the change of a larger population, we begin by estimating the monthly population at the national level by age, sex, race, and Hispanic origin. We then produce estimates of the total annual populations of counties, which we sum to the state level. With the national characteristics, state total, and county total estimates created, we produce estimates of states and counties by age, race, sex, and Hispanic origin. One of our key estimates principles is that all of the estimates we produce must be consistent across geography and demographic characteristics. For example, the sum of the county total populations must equal the total national population, and the sum of a particular race group within a state's counties must equal the total of that particular race group in the state. Since our various estimates products and processes use slightly different input data and methodology, they often do not generate this consistency automatically. Consequently, we adjust the nal estimates to be consistent. As a result, the demographic components of change do not account for all of the year-to-year change in the estimates series. We call the difference between the result of the balancing equation and the final estimate the residual. The national population estimates by characteristics do not contain a residual. This is because they are made first and are not required to sum to any pre-defined total. The balancing equations for the subnational processes initially produce what we call "uncontrolled\" estimates. In order to ensure consistency, we use a process called controlling or raking. This involves calculating a rake factor as the control total (to which data must sum) divided by the sum of the numbers we wish to control (the initial estimated values). R k _( Control Total ) a B ECUncontrolied Values) We multiply this rake factor by the uncontrolled values to generate "controlled\" estimates. In the simple case where the goal is to sum to a column total, this is fairly straightforward. However, deriving state and county population estimates by characteristics requires a slightly more complicated process. Since we produce national estimates by characteristics and state/county totals first, state and county characteristics need to use a two-way raking system. For example, state characteristics are required to be consistent with national characteristics and state total estimates (see the section on state and county characteristics). The controlling process usually produces estimates that sum to a predefined total but are not integers. Because we require estimates in integer form, we round these data to remove the decimal values. Applying a simple rounding algorithm may upset the consistency established in the controlling process. To account for this, we use a variety of controlled rounding procedures {e.g., greatest mantissa or two-way controlled rounding)