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Expert: Alon Mandes - 4/16/2009


Question
I have a relative growth function 1/P∙dP/dt= b + aP where a = -.00009175 and b = .02866 and P = 3.9. P shold appear only on one side.
1/P∙dP/dt= .02866 + -.00009175P I was told I need to separate variables so that all P terms are on one side and all t terms (dt) are on the other. I was told to integrate one side with respect to P and the other with respect to t. They say I need to use partial fractions. The final answer should set P(t) equal to some function of t.  

Answer
(1/P)∙[dP/dt]=b+aP
dP/dt=bP+bP²

dP        dt
------- = ----
bP+bP²     1

∫dP/(bP+bP²) = t+C .

Now , The I will give you the answer, but you will have to prove it
by yourself : ∫dP/(bP+bP²)=(1/b)*Ln[P/(bP+a)] . Thus,
(1/b)*Ln[P/(bP+a)]=t+C
Ln[P/(bP+a)]=bt+bC
P/(bP+a)=e^(bt+bC)
P=(bP+a)e^(bt+bC)
P-bPe^(bt+bC)=ae^(bt+bC)
P[1-e^(bt+bC)]=ae^(bt+bC)


          ae^(bt+bC)
P(t)  =   -------------
         [1-e^(bt+bC)]
    
Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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