Because the question doesn't have a best answer selected, I will give it a try.
We know that the number of b's is somewhere between number of a's and twice the number of a's.
Now let's design a PDA for this,
Push all the a's into the stack and when the b's start to come,
At this point you have to make a copy of this machine, one copy will pop 1 a for 1 b and the other will pop 1 a for the 2 b's.
As another b comes, make 2 copies of the each of the earlier 2 machines, one would pop 1 a for 1 b and the other would pop 1 'a' for 2 b's.
Similarly, we keep on making 2 copies of machine at each occurrence of b. And the same would continue until any one of the machines accept the string or all of them reject the string after the end of the input.
if you're able to imagine, we would get a binary tree like structure.
Since here we're creating copies of the PDA, it can't be a DPDA, so not a DCFL but just CFL.