--- title: "Population 2070 by three methods, demand 2080" subject: "Water Supply Engineering" chapter: 3 key: "semester_5/water_supply_engineering:pop-bk80" source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-bk80 site: BCT Engineering --- # Population 2070 by three methods, demand 2080 Water Supply Engineering · Chapter 3: Quantity of Water - Asked in: 2080 Baisakh, 8 marks - Video: [FORECAST THE POPULATION OF GIVEN YEAR- WATER SUPPLY ENG. 4TH SEMESTER @Er.dipesh186 NUMERICAL](https://www.youtube.com/watch?v=EsTkhEvqRDg) — Er. Dipesh Bhatt - 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-bk80 - Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3 ## Question Determine the population of a city in the year 2070 by (a) Arithmetical increase method, (b) Geometrical increase method, (c) Decrease rate growth rate method. The census population of the city is as follows: | Year | 2010 | 2020 | 2030 | 2040 | 2050 | |---|---|---|---|---|---| | Population | 25,000 | 35,000 | 45,000 | 55,000 | 60,000 | Also calculate the total water demand for the city in 2080. ## Short answer Arithmetical method: 77,500; geometrical method: 92,952; decreasing rate method: 52,447. For 2080, design population is average 80,983, giving water demand 8,908 m³/day (103.1 L/s). ## Answer The census interval is 10 years (B.S.) and the last census is 2050. For 2070, $n = 2$ decades. #### Population in 2070 **Arithmetical increase method** Average increase per decade: $\bar x = \dfrac{60{,}000-25{,}000}{4} = 8{,}750.0$ $$ P_{2070} = P_n + n\bar x = 60{,}000 + 2\times 8{,}750.0 = 77{,}500 $$ **Geometrical increase method** Average growth rate per decade (geometric mean): $r = \left(\dfrac{60{,}000}{25{,}000}\right)^{1/4}-1 = 24.467\%$ $$ P_{2070} = P_n(1+r)^n = 60{,}000\times(1+0.24467)^{2} = 92{,}952 $$ **Decreasing rate of growth method** | Decade | Increase | Growth rate (%) | Decrease in rate (%) | |---|---|---|---| | 2010-2020 | 10,000 | 40.00 | - | | 2020-2030 | 10,000 | 28.57 | 11.43 | | 2030-2040 | 10,000 | 22.22 | 6.35 | | 2040-2050 | 5,000 | 9.09 | 13.13 | Average decrease in rate $= 10.303\%$ per decade. | Year | Growth rate (%) | Population | |---|---|---| | 2060 | -1.21 | 59,273 | | 2070 | -11.52 | 52,447 | $P_{2070} = 52{,}447$ Because the growth rate falls sharply in the last decade, this method predicts a falling population, which should be treated with caution for a growing city. | Method | Population in 2070 | |---|---| | Arithmetical increase | 77,500 | | Geometrical increase | 92,952 | | Decreasing rate of growth | 52,447 | #### Population in 2080 (n = 3) | Method | Population in 2080 | |---|---| | Arithmetical increase | 86,250 | | Geometrical increase | 115,694 | | Decreasing rate of growth | 41,004 | #### Water demand in 2080 The per capita demand is not given, so 110 lpcd is assumed for a city. The last increment (5,000) is much smaller than the earlier ones, so growth is slowing; the methods give very different results, and the average of the three is adopted as the design population. $$ P_{2080} = \frac{86{,}250+115{,}694+41{,}004}{3} = 80{,}983 $$ $$ Q = 80{,}983\times110 = 8{,}908{,}094\ \mathrm{l/day} = 8{,}908\ \mathrm{m^3/day} $$ **Answer: Population in 2070: arithmetical 77,500, geometrical 92,952, decreasing rate 52,447. Water demand in 2080 = 8,908 m$^3$/day (103.1 l/s).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does the decreasing rate method give a falling population by 2070? A. Average decrease in rate (10.3%) pushes the growth rate negative B. Census values are negative C. The arithmetic increase is negative D. n is negative Answer: A. Growth rate 9.09% minus 10.3% per decade becomes negative (-1.21%, -11.52%). (Key point: Decreasing rate trend) 2. What is the arithmetical forecast for 2070? A. 60,000 B. 92,952 C. 77,500 D. 85,000 Answer: C. 60,000 + 2 x 8,750 = 77,500. (Key point: Arithmetical result) 3. What is n for 2080 with last census 2050? A. 2 B. 3 C. 4 D. 0.3 Answer: B. (2080-2050)/10 = 3 decades. 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