The Downtown Business Association (DBA) in a certain city plans to increase its ...

Choice A is correct. The DBA plans to increase its membership by n businesses each year, so x years from now, the association plans to have increased its membership by nx businesses. Since there are already b businesses at the beginning of this year, the total number of businesses, y, the DBA plans to have as members x years from now is modeled by y = nx + b.

Choice B is incorrect. The equation given in choice B correctly represents the increase in membership x years from now as nx. However, the number of businesses at the beginning of the year, b, has been subtracted from this amount of increase, not added to it. Choices C and D are incorrect because they use exponential models to represent the increase in membership. Since the membership increases by n businesses each year, this situation is correctly modeled by a linear relationship.