Program Description: Purpose of the problem is to fit the logistic equation to the actual U.S. population data for the years 1850, 1900 and 1950. Also solve the resulting logistic equation and compare the predicted and actual population for the years 1990 and 2000. Summary introduction: The logistic equation to any three population values P 0 , P 1 and P 2 corresponding to equally spaced times t 0 = 0 , t 1 and t 2 = 2 t 1 can be obtained by the evaluation of k = − 1 M t 1 ln ( P 0 ( M − P 1 ) P 1 ( M − P 0 ) ) and M = P 1 ( 2 P 0 P 2 − P 0 P 1 − P 1 P 2 ) P 0 P 2 − P 1 2 . The logistic equation is P ( t ) = P 0 M P 0 + ( M − P 0 ) e − k M .

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Chapter 2.1, Problem 37P

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Program Description:Purpose of the problem is to fit the logistic equation to the actual U.S. population data for the years 1850, 1900 and 1950. Also solve the resulting logistic equation and compare the predicted and actual population for the years 1990 and 2000.

Summary introduction: The logistic equation to any three population values $P0$ , $P1$ and $P2$ corresponding to equally spaced times $t0=0$ , $t1$ and $t2=2t1$ can be obtained by the evaluation of $k=−1Mt1ln(P0( M− P 1 )P1( M− P 0 ))$ and $M=P1(2P0P2−P0P1−P1P2)P0P2−P12$ . The logistic equation is $P(t)=P0MP0+(M−P0)e−kM$ .

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