During the period from 1790 to 1930, the U.S. population P
Chapter , Problem 65(choose chapter or problem)
During the period from 1790 to 1930, the U.S. population P .t / (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P .t / remained close to the solution of the initial value problem dP dt D 0:03135P 0:0001489P2; P .0/ D 3:9: (a) What 1930 population does this logistic equation predict? (b) What limiting population does it predict? (c) Has this logistic equation continued since 1930 to accurately model the U.S. population? [This problem is based on a computation by Verhulst, who in 1845 used the 17901840 U.S. population data to predict accurately the U.S. population through the year 1930 (long after his own death, of course).]
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