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Rate of Change

The rate of change ROC is a ratio used to compare how a variable changes in relation to another variable. It is determined by dividing the change in the output variable by the change in the input variable For any ordered pairs and the rate of change is calculated using the following formula.

The Greek letter (Delta) is commonly used to represent a difference. This leads to an alternative way of writing the formula for ROC.

Consider when the rate of change is constant. In these cases, the function is linear. Then, the rate of change refers to the slope of the line of the function's graph.


Positive, Negative, and Zero Rate of Change

Depending on the relationship between the variables, the rate of change can be positive, negative, or zero.

Positive rate of change: As the independent variable x increases, the dependent variable y also increases; Negative rate of change: As the independent variable x increases, the dependent variable decreases; Zero rate of change: As the independent variable x increases the dependent variable y stations unchanged.


Rate of Change Units

The units of a rate of change are the ratio of output units to the input units, meaning that they are derived units. Interpreting the rate of change depends on the context.

Output Units Input Units Rate of Change Units Possible Interpretation
meters seconds Car speed over a certain period of time
bacteria hours Growth rate of bacteria in an experiment
U.S. dollars hours Worker's hourly wage