Question

If M(0)=1000 and dM/dt=20000M-20M^2 then the limit of M(t) as t approaches infinity is zero, 1000, 2000, 20000, or non-existent?

Answer 1

If you try to find the general solution, you get
\[
M(t)=\frac{1000 e^{20000 t}}{e^{1000 C}+e^{20000 t}}
\]

Answer 2

\[
M(0)=\frac{1000}{e^{1000 C}+1}
\]
For which values of C, M(0)=1000?
If you know the answer , them you can finish it.

Answer 3

Is there such a C?