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# Rate of Change Formula

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. Let us learn about the rate of change formula with a few examples in the end.

## What Is the Rate of Change Formula?

The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to coordinates of x can found out as Δy/ Δx = (y_{2 }- y_{1 })/ (x_{2 }- x_{1 }). For a linear function, the rate of change m is represented in the slope-intercept form for a line: y=mx+b whereas the rate of change of functions is otherwise defined as, (f(b)-f(a))/ b-a

### Rate of Change Formula

- Formula 1: The basic formula for the rate of change is:

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

- Formula 2: Formulas of rate of change in algebra

Δy/ Δx = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

- Formula 3: Rate of change of functions

(f(b)-f(a))/ b-a

## Applications of Rate of Change Formula

The rate of change tells us how something changes over time.

- Distance traveled by car in a certain amount of time.
- The current through an electrical circuit increases by some amperes for every volt of increased voltage.
- It is considered an important financial concept as well. It allows investors to spot security momentum and other trends.
- Work done per unit time.
- Work done and the number of people required for doing it

Let us have a look at a few solved examples to understand the rate of change formula better.

## Examples Using Rate of Change Formula

**Example 1:** Using the rate of change formula, calculate the rate of change for the following information in the table:

Time Driving (in hr) | Distance Travelled (in miles) |
---|---|

2 | 40 |

4 | 180 |

**Solution:**

To find: Rate of change

Using the rate of change formula,

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

Rate of change = (Change in distance) / (Change in time)

Rate of change = (180-40) / (4-2)

Rate of change = (140) / (2)

Rate of change = 70

**Answer: The rate of change is 70 or the rate of change of distance with time is 70 miles per hour.**

**Example 2:** Calculate the rate of change for the following information in the table:

Time (in days) | Height of the tree (in inches) |
---|---|

50 | 4 |

140 | 7 |

**Solution:**

To find: Rate of change.

Using the rate of change Formula,

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

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

Rate of change = (7-4) / (140-50)

Rate of change = (3) / (90)

Rate of change = 1/30 = 0.033..

**Answer: The rate of change is 0.033 or the rate of change of height of the tree with time in days is 0.033 inches per day.**

**Example 3:** Find the rate of change for the situation: Ron completed 3 math assignments in one hour and Duke completed 6 assignments in two hours.

Solution:

To find: Rate of change.

Using the rate of change Formula,

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

Rate of change = (Change in assignments done) / (Change in hours)

Rate of change = (6-3) / (2-1)

Rate of change = (3) / (1)

Rate of change = 3/1 = 3 assignments/hour

**Answer: The rate of change is 3.0 or the rate of change of assignments done with time in hours is 3 assignments per hour.**

## FAQs on Rate of Change Formula

### What Is the Formula for Rate of Change in Math?

A rate of change formula is used to calculate the rate which describes how one quantity changes in relation to the change in another quantity. Thus, the formula for the rate of change is, ROC = (Change in quantity 1) / (Change in quantity 2)

### What Is the Average Rate of Change Formula?

The average rate is the total change divided by the time taken for that change to occur. The way it is calculated is similar to how the average velocity of an object is calculated. For example, the average rate of change in a population of an area can be calculated with only the times and populations at the start and end of the period.

### How To Use the Rate of Change Formula for Graphs?

The rate of change can be depicted and calculated using the formula for rate of change, that is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), commonly known as slope formula.

### What Is the Instant Rate of Change Formula?

The instantaneous rate of change is defined as the change in the rate at a particular instant. It can be considered the same as the change in the derivative value at a specific point. For a graph, the instantaneous rate of change at a specific point is the same as the tangent line slope.

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