Question

Analyze the long term behavior if Diff Eq

Answer 1

\[Q'(t)=\frac{ r }{ 4 }-\frac{ r }{ 100 }Q(t)\]

Answer 2

by examining the signs of the right hand side

Answer 3

@ganeshie8

Answer 4

After solving this ODE, you get
Q(t) = \(-\dfrac{1}{re^{0.01r(t+C_1)}}+25\)
after a long time, that means take lim of Q(t) when t goes to infinitive, the first term =0, so that Q(t) =25

Answer 5

I got that

Answer 6

so 25 is critical point

Answer 7

what are the signs