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Assumptions
The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The period intervening the points of known data and the point for which an estimate is required is also considered to be a normal period.
For instance, when we require the interpolation of the population figure for the year 1985, we assume that between 1981 and 1985 there have been no cause for sudden jumps or declines in population such as war, flood, famine, cyclone and the like.
It is also presumed that the increases and decreases take place only at a uniform rate.
For instance, if the population in 1981, was 700 million and in 1991, 850 million, it is assumed that the accretion to the population has taken place at a steady growth rate.
Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is
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