Use P0 = 3.9 (1790 population) as your initial condition to find the particular solution for this differential equation. Note: You may find it easier to solve in terms of the constants a and b. Show all the steps in your solution.(adsbygoogle = window.adsbygoogle || []).push({});

This is the last step to a multi-part problem. I basically did a scatter plot of the population for each year (x) and the relative growth rate (y) which was found by dividing an approximate growth rate by the US population between 1790 and 2000, did a linear regression and obtained the equation below.

y = -.0000917x + .0287

Given (1/P)(dP/dt) = b +aP

(1/P)(dP/dt) = .0287 - .0000917(P)

I think I need to integrate and get 1/P(dt) = (.0287 - .0000917(P))/dP

I don't know if this is set up right to integrate and if it is the fractions are confusing me and I don't know where to start. Any help or suggestions would be appreciated. Thanks.

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# Homework Help: U.S. Population Modeling

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