ok so we have the problem...

ln N - ln(N-2000)= t + C

so i tried to say that ln a = ln B = ln (a/B)

so i got ln(N/N-2000)= t + c

so then i raised both sides to e and got

N/N-2000 = e^(t+c)

my final answer was -2000e^(t+c)/(1-e^(t+c))

my book got the same thing except their answer was positive, i dont see how this could be possible? can someone tell me where i went wrong