Rate of Change

What is Rate of Change?

Rate of Change is the measure of how quickly one variable moves in respect to another. The rate of change is visually displayed by the slope of the curve. It can be defined as a ratio between a change in the value and a resulting change in the other. The Greek letter ???? (delta) is the mathematical symbol frequently used to represent any rate of change.

Understanding Rate of Change

The rate of change describes the movement of a value that is used to numerically express the percentile change over a particular timeframe. The change is a measure of how quickly one frequency changes with respect to another. If the independent variable is x and the dependent variable is y, then As a result, the formula is as follows:


Rate  of  change = Change  in  y / Change  in  x


Change rates can be either positive or negative. Among the two variables, it refers to a rise or reduction in the y-value. The term "zero rate of change" refers to a value that does not vary with time.

Types of Rate of Change

Positive Rate

As the value of x rises so does the value of y, and the slope changes shape upward.

Negative Rate

The curve shifts downward as the value of x rises and the number of y falls.

Zero Rate

When the input value starts going up, the value of y stays the same. That is, the y value remains constant, and the curve is a straight stripe.

Applications of Rate of Change

The rate of change is a measurement of how quickly things evolve and change. Some applications of the rate of change are listed below-

  • In a given timeframe, the distance traveled by auto.
  • With every volt of specified capacity, the current across an electrical system grows by a few microamps.
  • It is also considered a very important formula to determine different financial factors. It enables investors to identify and detect dynamics as well as other patterns.
  • Work completed per unit of time.
  • The percentage of employees needed to complete a work.

The Importance of Rate of Change

Determining the rate of change is important, it allows us to change the reaction parameters to produce a more suited rate and more proper and effective responses.

In order to manage and control the entire process of marketplaces and segments within them, the rate of change is equally significant. It's crucial to keep track of opponents' goods or services renewal rates, major changes in their operations and driving innovation, and how quickly they can reorganize. 

These insights give people information about what change of rate they'll need to react effectively and what change of rate they'll need to form successfully, both of which are dependent on change. The theory of the rate of change is crucial in finance since it allows investors to detect market dynamics and other movements. 

In the immediate term, a property with high momentum or a positive ROC, for example, outranks the marketplace. An investment with a ROC that goes underneath the moving average, or one with a low average ROC, on the other hand, is liable to lose valuation and might be viewed as a sell indication by traders.

Practical Example

Example 1: Determine the rate of change for the given figures is given by using the rate of change equation:

Driving a bike (in hr)

Travelling Distance (in miles)





To find the rate of change we have to use the rate of change formula,

Rate of change = (Change in variable 1) / (Change in variable 2)

Rate of change = (Change in miles) / (Change in hr)

Rate of change = (200-80) / (7-4)

                         = (120) / (3)

                         = 40

So, the rate of change is 40.


Example 2: Calculate the rate of change for the data in the table below:

Time (in days)

Height of a plant (in inches)





To find the rate of change we have to use the rate of change formula,

Using the rate of change Formula,

Rate of change = (Change in variable 1) / (Change in variable 2)

Rate of change = (Change in height of the plant) / (Change in days)

Rate of change = (15-7) / (150-60)

                         = (8) / (90)

                         = 0.0889

So, the rate of change of height of the plant with time in days is 0.0889 inches per day.

In Sentences

  • Rate of change is commonly used in mathematics and other sectors to determine how a change in one variable can affect the other. 


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