Help Finishing a Logistic Model

[pjallen58]

I am working on a population model using US population data. I have done a scatter plot, linear regression and now need to complete.

This is what I have:

y = .0287 - .0000917x

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

I have set this up to integrate and by keeping the variables a and b in the equation and using partial fractions get:

ln |P/(b + aP)| = bt + bC

ln |P/(.0287 - .0000917P)| = .0287t + .0287C

at t = 0, P0 = 3.9, so C = 1/.0287 ln 137.6

ln |P/(.0287 - .0000917P)| = .0287t + ln 137.6 the take exponential of each side

P/|.0287 - .0000917P| = 137.6e^.0287t

This is where it gets confusing. I pulled a P out of the denominator to get only one P

P/P|.0287/P - .0000917| = 137.6e^.0287t

1/|.0287/P - .0000917| = 137e^.0287t

I think I should swap the denominator on the left with the numerator on the right but not sure if I can do this with "e". Any advice or suggestions would be appreciated. Thanks.

 

[Defennder]

Why can't you do that with e?