Arithmetical Increase Method vs Geometrical Increase Method

Arithmetical increase method and geometrical increase method are two commonly used methods for forecasting population growth. Let us compare these methods and understand why the arithmetical increase method gives a lesser value compared to the geometrical increase method.

Arithmetical Increase Method

In the arithmetical increase method, the increase in population is assumed to be constant over a given period of time. The method involves adding a fixed value to the initial population to calculate the population for subsequent years. For example, if the population of a city is 100,000 in 2010 and it is assumed that the population will increase by 10,000 every year, then the population in 2015 will be:

Population in 2015 = 100,000 + (10,000 x 5) = 150,000

Geometrical Increase Method

In the geometrical increase method, the increase in population is assumed to be proportional to the existing population. The method involves multiplying the initial population by a certain factor to calculate the population for subsequent years. For example, if the population of a city is 100,000 in 2010 and it is assumed that the population will increase by 10% every year, then the population in 2015 will be:

Population in 2015 = 100,000 x (1.1)^5 = 161,051

Comparison

Now, let us compare the two methods and understand why the arithmetical increase method gives a lesser value compared to the geometrical increase method.

- The arithmetical increase method assumes a constant increase in population over time, whereas the geometrical increase method assumes a proportional increase in population.
- The arithmetical increase method is suitable for short-term forecasting, whereas the geometrical increase method is suitable for long-term forecasting.
- The arithmetical increase method gives a linear increase in population, whereas the geometrical increase method gives an exponential increase in population.
- The arithmetical increase method gives a lower value compared to the geometrical increase method because it assumes a constant increase in population, which is less than the proportional increase assumed by the geometrical increase method.

Conclusion

In conclusion, the arithmetical increase method gives a lesser value compared to the geometrical increase method because it assumes a constant increase in population, which is less than the proportional increase assumed by the geometrical increase method. The choice of method depends on the purpose of forecasting and the time frame for which the forecast is required.