dP/dt = 0.02P, P(0)=20.

Because the initial condition gives P as some function of t. and we know that when t = 0, P = 20.

Think of P as being P(t)........kind of like  "f(x)" that you were used to dealing with in Algebra.

Separating the variables and integrating, we have

∫1/P  dp  =  ∫.02 dt

ln P = .02t + C

This says that

e^(.02t + C) = P    .....or.....

(e^C)* e^(.02t) = P

And e^C is just a constant....we can just call it "C"

And we have P(0) = 20   .... so...

Ce^(.02(0)) = 20

 Therefore, C = 20

And our answer is

P = 20e^(.02t)

I hope this helps.....

What makes you solve it as P= and move everything else?

It is easier also.