Population 2088 by three methods, design year demand

The census data are arranged in ascending order of year (2028 to 2068). Interval 10 years; for 2088, $n = 2$ decades.

Population forecast

Arithmetical increase method

Average increase per decade: $\bar x = \dfrac{65{,}500-29{,}000}{4} = 9{,}125.0$

$$P_{2088} = P_n + n\bar x = 65{,}500 + 2\times 9{,}125.0 = 83{,}750$$

Geometrical increase method

Average growth rate per decade (geometric mean): $r = \left(\dfrac{65{,}500}{29{,}000}\right)^{1/4}-1 = 22.592\%$

$$P_{2088} = P_n(1+r)^n = 65{,}500\times(1+0.22592)^{2} = 98{,}438$$

Decreasing rate of growth method

Average decrease in rate $= 4.225\%$ per decade.

$P_{2088} = 77{,}186$

Design population and water demand

The design year is 2088 BS. The mean of the three methods is adopted as design population:

$$P_{2088} = \frac{83{,}750+98{,}438+77{,}186}{3} = 86{,}458$$ $$Q = 86{,}458\times120 = 10{,}374{,}966\ \text{l/day} = 10{,}375\ \mathrm{m^3/day}$$

Answer: Design year = 2088 BS; design population = 86,458; total water demand = 10,375 m$^3$/day (120.1 l/s).