If the derivation has atleast ${2^b}$ derivations , then since the grammar is in Chomsky Normal Form, then the length of the string is atleast ${2^b}$ $\Rightarrow$ the height of the tree is atleast b+1. Now from the Proof of Pumping Lemma(Not in Sipser, but in Hopcroft-Ullman) you can find that we can pump any number of strings , i.e the language is infinite.