Limiting Value of P as t Approaches Infinity

[nick.martinez]

What is the limiting value of P as t->infinity

dp/dt=0.4P(10-P)

My attempt at the solution was to serperate the function and get each side in terms of one variable

dp/(P(10-P)) = 0.4/dt

[-ln(|p-10|/|p|)]/10=0.4t

-ln(|p-10|/|p|)=4t
take e^ of both sides of equation

(p-10/p)=e^4t and we know that the equation is undefined on the left when the p=10 therefore there is some type of discontinuity. is this correct?

 

[mfb]

dp/(P(10-P)) = 0.4/dt

I think this should be 0.4 dt.
The following line is missing an integration constant.

(p-10/p)=e^4t and we know that the equation is undefined on the left when the p=10 therefore there is some type of discontinuity. is this correct?

That equation is problematic if you want to take the limit of t->infinity. There are better ways to do this, but you can guess the value of p here as well. Oh, and there are brackets missing.