Final answer:
A visitor to Muncie, Indiana, observing the Ball family's prominent presence in various local institutions would find that the power-elite model accurately describes this influence.
Step-by-step explanation:
The political model that best explains a situation where a family's name is associated with multiple businesses and institutions in a community is a. The power-elite model. This model posits that a small number of people, typically those who are wealthy or have strong business ties, disproportionately influence and control public institutions and resources, which appears to be the case with the Ball family's prominence in Muncie, Indiana. The evidence supports the elite theory of government, where the elite hold sway over significant community assets, like a university, bank, and hospital, which suggests that they might also have considerable influence over local politics and economy.