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4.2 Design Population 123
For retardant, arithmetic progression,

y y (1>n) ln(1 nk t) (4.12)
0
0
These and similar equations are useful in water and wastewater practice, especially in
water and wastewater treatment kinetics.

4.2.3 Short-Term Population Estimates
Estimates of midyear populations for current years and the recent past are normally derived by
arithmetic from census data. They are needed perhaps most often for (a) computing per capita
water consumption and wastewater release, and (b) for calculating the annual birth and general
death rates per 1,000 inhabitants, or specific disease and death rates per 100,000 inhabitants.
Understandably, morbidity and mortality rates from waterborne and otherwise water-
related diseases are of deep concern to sanitary engineers.
For years between censuses or after the last census, estimates are usually interpolated
or extrapolated as arithmetic or geometric progressions. If t and t are the dates of two se-
i
j
quent censuses and t is the midyear date of the year for which a population estimate is
m
wanted, the rate of arithmetic growth is given by Eq. 4.9 as
k arithmetic y y >(t t )
j
j
i
i
and the midyear populations, y , of intercensal and postcensal years are as follows:
m
Intercensal:
y y (t t )(y y )>(t t ) (4.13)
i
i
m
j
i
j
i
m
Postcensal:
Y y (t t )(y y )>(t t ) (4.14)
j
i
j
j
j
m
i
m
In similar fashion, Eq. 4.8 states that
k arithmetic (log y log y )>(t t )
j
j
i
i
and the logarithms of the midyear populations, log y , for intercensal and postcensal years
m
are as follows:
Intercensal:
log y log y i (t m t i )(log y j 1og y i )>(t j t i ) (4.15)
m
Postcensal:
log y m log y j (t m t j )(log y j log y i )>(t j t i ) (4.16)
Geometric estimates, therefore, use the logarithms of the population parameters in the
same way as the population parameters themselves are employed in arithmetic estimates;
moreover, the arithmetic increase corresponds to capital growth by simple interest, and
the geometric increase to capital growth by compound interest. Graphically, arithmetic
progression is characterized by a straight-line plot against arithmetic scales for both
population and time on double-arithmetic coordinate paper and, thus, geometric as well as
first-order progression by a straight-line plot against a geometric (logarithmic) population
scale and an arithmetic timescale on semilogarithmic paper. The suitable equation and
method of plotting are best determined by inspection from a basic arithmetic plot of
available historic population information.