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# Logistic Curve Method of Population Forecasting with Solved Example

The logistic curve method of __population forecasting__ is a method to predict the population using the logistic curve of population growth. The concept of logistic curve and formulas to predict the population as per the logistic curve method are discussed further.

## What is a Logistic Curve

In an ideal environment, populations grow at an exponential rate. The growth curve of these populations is smooth and becomes increases steeply over time. However, exponential growth is not possible because of factors such as limitations in food, competition for other resources, disease etc. Populations eventually reach the carrying capacity or saturation capacity of the environment, causing the growth rate to slow nearly to zero. This produces an **S-shaped curve** of population growth known as the logistic curve.

## Logistic Curve Method

As discussed, this method uses the logistic curve of population growth. Therefore, it uses the equation of the logistic curve to directly predict the population. Equation of the logistic curve is given as,

** P = Ps/(1+(m*ln^-1(n*t))), **pictorial representation of the same is shown below,

where,

*m = (Ps - Po)/Po,*

Ps - saturation population given by, ** Ps = (2*Po*P1*P2 - P1^2(Po+P2))/(Po*P2 - P1^2)**,

pictorial representation of the same is shown below,

** n = (1/t1)*ln((Po*(Ps-P1))/(P1*(Ps-Po))**, pictorial representation of the same is shown below,

Po - population at to years,

P1 - population at t1 years,

P2 - population at t2 years,

t1 - number of years between to and t1,

t2 - number of years between to and t2,

t - number of years between 'to' and required year,

t2 = 2*t1 (in general).

## Solved Example

**Question:** Using the data given below find the population for the year 2021.

Year | Population |

1991 | 80000 |

2001 | 250000 |

2011 | 480000 |

**Solution:**

Step 1: Given data,

Po = 80,000 at to = 0 years,

P1 = 250,000 at t1 = 10 years,

P2 = 480,000 at t2 = 20 years,

Step 2: Find saturation population Ps using the formula ** Ps = (2*Po*P1*P2 - P1^2(Po+P2))/(Po*P2 - P1^2)**,

**Ps = 655,602**

Step 3: Find the value of m using the formula *m = (Ps - Po)/Po,*

m = (655602 - 80000)/80000

**m = 7.195**

Step 4: Find the value of using the formula *n = (1/t1)*ln((Po*(Ps-P1))/(P1*(Ps-Po)),*

**n = -0.1489**

Step 5: Find the population for the required year using the formula *P = Ps/(1+(m*ln^-1(n*t))),*

t = 30 (number of years between to and t)

P = 655602/(1 + (7.195*ln^-1(-0.1489*30)))

**P = 6,05,436 is the population for the year 2021.**

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**Practise Problem **

For more insights and to know more about other population forecasting methods refer to the video lecture below.

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