How long does it take for black mold to develop in an attic of a home?

We hired a home inspector before we bought our house. He said that the attic was fine. A month after his inspection, we found widespread black mold on the eves of the unfinished portion of the attic. The home inspector claimed that the mold must have grown in the four weeks between his inspection and our finding it. Is this possible or is he just trying to cover his carelessness?