# calculus – Assuming limits in a linear derivative equation

Hi, I don’t understand the reasoning behind the limits of $$0<= P(0) <= M$$, and for the k>0, I only managed to figure out that K can’t be equaled to 0. But maybe it’s because I did it in a different method from the book? I used the same $$I(t)$$ so got up to:

$$e^{kt}p = KMe^{Kt}$$

$$e^{kt}p = int Ae^{Kt}$$, where $$A = KM$$

$$e^{kt}p = frac AK e^{Kt}$$, doing a u sub where $$u=Kt$$

From there, if you sub in KM into A, K can’t be 0. But how did they assume the rest? Thanks