Final answer:
Rate of change can be applied to multiple fields such as chemistry, meteorology, and economics, demonstrating its utility in understanding reaction rates, weather patterns, and growth rates. Custom formulas can also be developed to account for complex variables in productivity measurement.
Step-by-step explanation:
To synthesize features of the rate of change for other applications, we can use the concept of rate of change beyond just measuring productivity. For example, in chemistry, the rate of a reaction can be expressed in terms of the rates of change in the concentrations of reactants and products over time. In meteorology, vector calculus can be employed to find the rate of change in atmospheric temperature, wind speed, and direction, although it is not used to measure changes in average rainfall. In economics, compound interest and compound growth rates are instances where small percentage point changes can have a significant impact, akin to productivity rates. To demonstrate the versatility of the rate of change, we could create a new formula possibly accounting for variables that affect productivity, such as the quality of artifacts produced or efficiency improvements over time.