# Average Rate of Change Formula

The average rate of change function describes the average rate at which one quantity is changing with respect to another. It is a measure of how much the function changed per unit, on average, in that particular interval. 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's look into the Average Rate of Change Formula in detail.

## What is Average Rate of Change Formula?

The Average Rate of Change function describes the average rate at which one quantity is changing with respect to something another quantity. The average rate of change formula is given as,

**A(x) = [f(b) - f(a)] / (b - a)**

### Average Rate of Change Formula

The average rate of change formula is given as,

A(x) = [f(b) - f(a)] / (b - a)

where,

- A(x) = Average rate of change
- f(a) = Value of function f(x) at a
- f(b) = Value of function f(x) at b

## Examples Using Average Rate of Change Formula

**Example 1: Calculate the average rate of change of a function, f(x) = 2x + 10 as x changes from 3 to 7 using the Average Rate of change formula.**

**Solution:**

Given:

f(x) = 2x + 10

a = 3

b = 7

f(3) = 2(3) + 10

f(3) = 6 + 10

f(3) = 16

f(7) = 2(7) + 10

f(7) = 14 + 10

f(7) = 24

Using the average rate of change formula,

A(x) = [f(b)−f(a)] / (b−a)

A(x) = [f(7)−f(3)]/ (7−3)

A(x) = (24 - 16) / 4

A(x) = 8/4

A(x) = 2

Therefore, the rate of change is 2 units.

**Example 2: Calculate the average rate of change of the function f(x) = x ^{2} – 5x in the interval 4 ≤ x ≤ 8.**

**Solution:**

Given: f(x) = x^{2} – 5x

a = 4

b = 8

f(4) = f(4) = (4)^{2} – 5(4) = 16 – 20 = -4

f(8) = f(8) = (8)^{2} – 5(8) = 64 – 40 = 24

Using the average rate of change formula,

A(x) = [f(b)−f(a)] / (b−a)

= (24−(−4)) / (8−4)

= 28/4

= 7

Therefore, Rate of change A(x) = 7 units.

**Example 3: Using the average rate of change formula, calculate the rate of change of a function, f(x) = 25x + 18 as x changes from 5 to 8**

**Solution: ** Given,

f(x) = 25x + 18, a = 5 and b = 8

f(5) = 25×5 + 18 = 143

f(8) = 25×8 + 18 = 218

Using the average rate of change formula,

A(x) = [f(b)−f(a)] / (b−a)

= [218 - 143] / (8 - 5)

= 75 / 3

= 25

Therefore, the average rate of change A(x) = 25

## FAQs on Average Rate of Change Formula

### What is Meant by Average Rate of Change Formula?

The average rate of change function describes the average rate at which one quantity is changing with respect to another. It is a measure of how much the function changed per unit, on average, in that particular interval. 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. The formula is A(x) = [f(b) - f(a)] / (b - a)

### What is the Formula to Find the Average Rate of Change?

The average rate of change formula is given as,

A(x) = [f(b) - f(a)] / (b - a)

where,

- A(x) = Average rate of change
- f(a) = Value of function f(x) at a
- f(b) = Value of function f(x) at b

### What is the Formula to Find the Rate of Change?

For a linear function, the rate of change is represented by the parameter (m) in the slope-intercept form for a line: y=mx+b, and is visible in a table or on a graph.

### Is the Average Rate of Change the Same as Slope?

The slope is considered as the average rate of change of a point where the average is taken and is reduced to zero. The slope is the rise or the fall over the run which is defined as the average rate of change in y coordinates over the change in x coordinates.