Final answer:
The interaction between motivation and performance is complex and cannot be encapsulated in a simple equation. The effect of different types of rewards on motivation, and the expectation of these rewards, significantly influences individual performance.
Step-by-step explanation:
The equation that accurately describes how motivation interacts with other variables to influence performance does not have a one-size-fits-all answer, as it could vary depending on the context and the factors considered. However, based on research findings, performance can be influenced by a mix of intrinsic and extrinsic motivators. For example, while tangible rewards such as money could negatively impact intrinsic motivation, intangible rewards like praise may maintain or enhance it. Additionally, the expectancy of a reward plays a critical role: if an individual anticipates an extrinsic reward, this might reduce intrinsic motivation, whereas unexpected rewards might not have this effect.
None of the equations presented (a through d) encompasses all these nuanced findings about motivation and performance. It is important to note that motivation's role varies and cannot be simplified into a single formula.