Trying to predict US population

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Homework Statement


I'm given a table of census data for the US. I'm supposed to construct a logistic population model using these numbers: (t in decades and population in millions) P(0) = 3.929, P(6) = 23.192, and P(12) = 91.972


Homework Equations


dP = P(a - bP)
dt

P(t) = aP0/(bP0 + (a - bP0)e-at)



The Attempt at a Solution


I've been working on it for several hours now. I tried to make a system of equations but the ex factor is fowling it up. I used http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/moreApps/logistic.html" model but it didn't give very accurate numbers. I have 3 pages of marked out numbers and no good answers to show for it. How do I find the constants a and b?
 
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