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Concept

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

y

by the change in the input variable

x .

For any ordered pairs

(x_{1}, y_{1})

and

(x_{2}, y_{2}),

the rate of change is calculated using the following formula.

Rate of Change Rate of Change = \frac{Change in y}{Change in x} = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

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

$Rate of Change = \frac{Δ y}{Δ x}$

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.

Extra

Positive, Negative, and Zero Rate of Change

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

Extra

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	$\frac{meters}{second}$	Car speed over a certain period of time
bacteria	hours	$\frac{bacteria}{hour}$	Growth rate of bacteria in an experiment
U.S. dollars	hours	$\frac{U . S . dollars}{hour}$	Worker's hourly wage

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