- APSEd

# Population Forecasting Methods | Formulas | Example Problems | Practice Problem

Population forecasting is a method to predict/forecast the future population of an area. Usually, the population at the __design period__ of water supply systems is predicted to find the water demand at that time, as the systems are required to fulfill their purposes till the end of the design period. Methods to predict the population are discussed further.

## Arithmetical Increase or Arithmetical Mean Method

### Where Arithmetical Increase Method is used

The arithmetical Increase Method is mainly adopted for **old and developed **towns**, **where the rate of population growth is nearly constant. Therefore, it is assumed that the rate of growth of the population is constant. It is similar to simple interest calculations. The population predicted by this method is the lowest of all.

### Arithmetical Increase Method Derivation

* dP/dt = K* (say), where, dP/dt represents rate of growth of population.

Integrating the above equation over P1 to P2 over a time period of t1 to t2,

*∫dP = K∫dt*

*[P2 - P1] = k * [t2 - t1]*

**P2 = P1 + K * Δt**

**P2 = P1 + x̄ * n**

* P2 = P1 + n*x̄

### Arithmetical Increase Method Formula

**Pn = Po + nx̄,**

where,

Po - last known population

Pn - population (predicted) after 'n' number of decades,

n - number of decades between Po and Pn and,

x̄ - the rate of population growth.

### Arithmetical Increase Method Example Problem

The following data (common data) will be used in the example problems for all other methods to be discussed.

Year | Population |

1930 | 25000 |

1940 | 28000 |

1950 | 34000 |

1960 | 42000 |

1970 | 47000 |

**Question: **With the help of the common data find the population for the year 2020 using the arithmetic increase method.

**Solution:**

Step 1: Find the increase in population each decade.

Year | Population | Increase |

1930 | 25000 | - |

1940 | 28000 | 3000 |

1950 | 34000 | 6000 |

1960 | 42000 | 8000 |

1970 | 47000 | 5000 |

Step 2: Find the average rate of increase of population (x̄)

x̄ = (3000+6000+8000+5000)/4

x̄ = 22000/4

x̄ = 5500

Step 3: Find the number of decades (n) between the last known year and the required year

n = 5 (5 decades elapsed between 1970 and 2020)

Step 4: Apply the formula **Pn = Po + nx̄,**

P[2020] = P[1970] + (5 * 5500)

P[2020] = 47000 + 27500

** P[2020] = 74,500**. Therefore, population at 2020 will be 74,500.

## Geometrical Increase Method

### Where Geometrical Increase Method is used

This method is adopted for **young and developing towns**, where the