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The following data represent the U.S. population from 1790 to 2010 . Find a dynamical system model that fits the data fairly well. Test your model by plotting the predictions of the model against the data. Year Population Year Population Year Population 1790 3,929,000 1870 38,558,000 1950 150,697,000 1800 5,308,000 1880 50,156,000 1960 179,323,000 1810 7,240,000 1890 62,948,000 1970 203,212,000
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In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation (d P)/(d t)=P(a-b P), where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation. | Numerade
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