I'm trying to solve this equation:
dN/dt = k(10 000 - N(t))
The attempt at a solution
dN/10 000 - N(t) = k dt
I integrate, and I'm left with:
- ln l10 000 - N(t)l = kt +C
I raise both sides with e. I don't know what e^- ln(xxx) is so I multiply both sides with -1
l10 000 - N(t)l = e^(-kt) * e^(-C) = -Ce^(-kt)
I now get the following:
N(t) = -10 000 - Ce^(-kt)
However the correct solution according to my book is:
N(t) = (+)10 000 - Ce^(-kt)
I am left with three questions:
1. What is e^- ln(...)?
2. Was I correct in making letting l10 000 - N(t)l = 10 000 + N(t) ?
3. What did I do wrong?