Final answer:
When determining the rate of change of one variable with respect to another, it is important to distinguish between independent and dependent variables. It is also important to understand the difference between instantaneous and average rates of change.
Step-by-step explanation:
When determining the rate of change of one variable with respect to another, it is important to distinguish between independent and dependent variables. The independent variable is the variable that is manipulated or controlled in an experiment, while the dependent variable is the variable that changes in response to the manipulation of the independent variable. For example, in the study comparing the number of motor vehicle fatalities with the age of drivers, the independent variable is the age of drivers and the dependent variable is the number of fatalities per 100,000 drivers.
In addition to distinguishing between independent and dependent variables, it is also important to understand the difference between instantaneous and average rates of change. The instantaneous rate of change refers to the rate of change at a specific point, while the average rate of change refers to the overall rate of change over a given interval. For example, in a displacement versus time graph, the instantaneous rate of change is represented by the slope of the tangent line at a specific point, while the average rate of change is represented by the slope of the secant line between two points.