Applied Mathematicsematics

Download Applied Mathematical Demography, Third Edition (Statistics by N. Keyfitz, Hal Caswell PDF

By N. Keyfitz, Hal Caswell

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Taking exponentials and then solving for N (t), and changing the constant to t0 = −c/r in order to locate the midpoint of the curve at t0 , we obtain a N (t) = . 1) 1 + e−r(t−t0 ) Pearl and others thought that fitting such a curve to a population time series would provide realistic short-term forecasts as well as estimates of the ultimate stationary population a. S. Census count with an error that was probably less than the error of the census itself. But the 1940 Census was a disappointment—it fell far below the curve, and the logistic was dropped amid a barrage of criticism no less intense than the earlier enthusiasm.

Euler provided an account that comes close to modern stable theory. 2 Logarithms to Various Bases The use of doubling time or half-life in such calculations is arbitrary; we might prefer to do the arithmetic by means of tripling time or one-third-life. 099/r. 303/r. 035 = 66 years, by 100 in 132 years, and so on. The number of doublings that correspond to a specified ratio of a final to an initial population is called the logarithm of that ratio to base 2 ; Thus the logarithm of 1000 to base 2 is the power to which 2 has to be raised to equal 1000.

693/n. 693/r, can be applied to show how nearly equal birth rates have been to death rates for most of human history. Our race must have started with a sizable group; and even if there had been periodic censuses at the time, questions of definition would have made their interpretation controversial. Suppose for this example that one human couple living a million years ago has multiplied to equal the present human total of about 4 billions, and that it has grown uniformly by geometric increase over the entire period.

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