I think it is because you are trying to multiply an int and a double, which I don't think it lets you do. Maybe try changing 'int k' to 'double k'.
Also, just a tip you could probably change the middle to a for loop, I don't know if that is better or worse but I think it makes more sense. For example:
Code:
while (population >= 0)
{
for (years = 0 /*That's already been stated but it doesn't matter*/; years <= 10000; years++)
{
population = pow(k*(initial_pop) - k*(initial_pop),2);
cout << years<<"\t"<<population << endl;
}
population = 0; // When years = 10,000 it will go here
cout << years<<"\t"<<population << endl;
}
Like I said, this isn't necessary and maybe you shouldn't use it in case you haven't learned it or something, but it's shorter and probably the better way.