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During the period from 1790 to 1930, the U.S. population
Chapter 2, Problem 29P(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 (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 1790-1840 U.S. population data to predict accurately the U.S. population through the year 1930 (long after his own death, of course).]
Questions & Answers
QUESTION:
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 (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 1790-1840 U.S. population data to predict accurately the U.S. population through the year 1930 (long after his own death, of course).]
ANSWER:SOLUTION:Step 1 of 5:In this question, during the period from 1790 to 1930, the U.S. population (t in years) grew from 3.9 million to 123.2 million. Throughout this period, remained close to the solution of the initial value problem .(a) Find what 1930 population does this logistic equation predict (b) Find what limiting population does it predict. (c)Find whether this logistic equation continued since 1930 to accurately model the U.S. population.