Yes that is the general form but it has to be shown from the basics of the question;

"Rate of increase of population directly proportional to number of people present"

Thus we can say,

Now this is a straight forward "seperate the variables and integrate" differential equation which gets to that general form.

Then sub in the conditions to work out the unknown constants: and the constant of integration which rightly said is and from that sub in to get the population in 2004.