Regular expression for string's of a's and b's beginning with b and not having two consecutive a's

Question

Question: Write a regular expression for the following language: "All strings of a's and b's in ∑^* beginning with b and not having two consecutive a's.

A textbook says the answer is (b+ba)^*. Shouldn't it be (b+ba)⁺ though, since if we included the star, it means we are accepting the empty string? And the empty string does not belong to the language above?

Thanks.