Businesses in nine San Francisco Bay Area counties will pay 4.4 cents for every ton of greenhouse gases they spew, after the district air-quality board voted 15-1 Wednesday to approve the fee. Set to take effect July 1, the fee will affect more than 2,500 businesses; the district estimates that perhaps seven power plants and oil refineries will have to pay more than $50,000 a year, but most businesses will pay less than $1. The fee is modest enough that dramatic emissions reductions are unlikely to occur, but proponents laud the precedent. Businesses were, unsurprisingly, less enthusiastic, expressing concerns about the cost of tracking and reporting emissions, duplication of state efforts to address warming, and the authority of an air-pollution board to regulate greenhouse-gas emissions. The fee is expected to generate $1.1 million in the first year, which will help pay for projects aimed at reducing the region’s emissions.