--- title: "Population 2021 and 2026, arithmetic and decreasing rate" subject: "Water Supply Engineering" chapter: 3 key: "semester_5/water_supply_engineering:pop-as69" source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-as69 site: BCT Engineering --- # Population 2021 and 2026, arithmetic and decreasing rate Water Supply Engineering · Chapter 3: Quantity of Water - Asked in: 2069 Asar - Video: [population forecasting, Arithmetic increase method with example, water supply engineering numericals](https://www.youtube.com/watch?v=7lSDFWfumqQ) — Civil Engineering Exam - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-as69 - Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3 ## Question Determine the population of the town in year 2021 and 2026 by (i) Arithmetic increase method and (ii) Decreased rate of growth method from the following details: | Year A.D. | 1961 | 1971 | 1981 | 1991 | 2001 | 2011 | |---|---|---|---|---|---|---| | Population | 18000 | 27000 | 38000 | 51000 | 66000 | 83000 | ## Short answer For 2021: arithmetic increase 96,000; decreased rate of growth 99,348. For 2026: arithmetic increase 102,500; decreased rate of growth 106,122. ## Answer Census interval 10 years; last census 2011. For 2021, $n = 1$ decade; for 2026, $n = 1.5$ decades. ### Population in 2021 (n = 1) **Arithmetical increase method** Average increase per decade: $\bar x = \dfrac{83{,}000-18{,}000}{5} = 13{,}000.0$ $$ P_{2021} = P_n + n\bar x = 83{,}000 + 1\times 13{,}000.0 = 96{,}000 $$ **Decreasing rate of growth method** | Decade | Increase | Growth rate (%) | Decrease in rate (%) | |---|---|---|---| | 1961-1971 | 9,000 | 50.00 | - | | 1971-1981 | 11,000 | 40.74 | 9.26 | | 1981-1991 | 13,000 | 34.21 | 6.53 | | 1991-2001 | 15,000 | 29.41 | 4.80 | | 2001-2011 | 17,000 | 25.76 | 3.65 | Average decrease in rate $= 6.061\%$ per decade. | Year | Growth rate (%) | Population | |---|---|---| | 2021 | 19.70 | 99,348 | $P_{2021} = 99{,}348$ ### Population in 2026 (n = 1.5) **Arithmetical increase method** Average increase per decade: $\bar x = \dfrac{83{,}000-18{,}000}{5} = 13{,}000.0$ $$ P_{2026} = P_n + n\bar x = 83{,}000 + 1.5\times 13{,}000.0 = 102{,}500 $$ **Decreasing rate of growth method** | Decade | Increase | Growth rate (%) | Decrease in rate (%) | |---|---|---|---| | 1961-1971 | 9,000 | 50.00 | - | | 1971-1981 | 11,000 | 40.74 | 9.26 | | 1981-1991 | 13,000 | 34.21 | 6.53 | | 1991-2001 | 15,000 | 29.41 | 4.80 | | 2001-2011 | 17,000 | 25.76 | 3.65 | Average decrease in rate $= 6.061\%$ per decade. | Year | Growth rate (%) | Population | |---|---|---| | 2021 | 19.70 | 99,348 | | 2031 | 13.64 | 112,896 | Population at 2026 is obtained by linear interpolation between the decade values: $P_{2026} = 106{,}122$. #### Summary | Method | 2021 | 2026 | |---|---|---| | (i) Arithmetic increase | 96,000 | 102,500 | | (ii) Decreased rate of growth | 99,348 | 106,122 | **Answer: Arithmetic increase: 2021 = 96,000, 2026 = 102,500. Decreased rate of growth: 2021 = 99,348, 2026 = 106,122.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For 2026 with last census 2011, n equals A. 15 decades B. 1.5 decades C. 0.5 decades D. 2.6 decades Answer: B. (2026-2011)/10 = 1.5. (Key point: Value of n) 2. Why is the average increase (83,000-18,000)/5? A. There are 5 census years in the data B. The design period is 5 decades C. There are 5 decade intervals between 6 census years D. It is the geometric mean Answer: C. Six census years form 5 intervals. (Key point: Arithmetic increase) 3. How is the 2021 growth rate 19.70% obtained? A. Last rate 25.76% minus average decrease 6.061% B. 25.76% plus 6.061% C. Average of all five rates D. 34.21% minus 6.061% Answer: A. Rate falls by the average decrease each decade. (Key point: Decreasing rate for 2021) 4. How is the 2026 population (decreased rate method) obtained? A. By using n = 1.5 in the arithmetic formula B. By taking the 2031 value C. By repeating the 2021 rate for 5 years D. By linear interpolation between the 2021 and 2031 populations Answer: D. 2026 is halfway between 2021 and 2031: 106,122. 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