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

### Question

The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of *n *businesses per year. There were *b *businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, *y*, the DBA plans to have as members *x *years from now?

### Options

The correct answer is A.

### Explanation:

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.

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